IFAC-PapersOnline

Robust Filtering for Uncertain Nonlinear Systems Satisfying a Sum Quadratic Constraint

04:00 PM Wednesday 31, 1969

This paper develops a robust extended Kalman filter for nonlinear uncertain systems with a deterministic description of noise and uncertainty. The system state dynamics are formulated in reverse time and the uncertainties are modeled in terms of sum quadratic constraints. The robust filtering problem is formulated as a set-valued state estimation problem which is recast into an optimal control problem. The solution of the resulting Hamilton-Jacobi-Bellman equation is obtained by using a quadratic approximation. This leads to an approximate information state for the filtering problem which is computed recursively through a difference Riccati equation derived by linearizing the observation equation and using a quadratic approximation to the system dynamics. The reduction of the robust estimator to the standard Kalman filter in the uncertainty-free linear case is also discussed.

The Development of a Randomised Unscented Kalman Filter

04:00 PM Wednesday 31, 1969

The paper deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the states, such as the extended Kalman filter, unscented Kalman filter or the cubature Kalman filter, are based on approximations which lead to biased estimates of the state and measurement statistics. The aim of the paper is to propose a new local filter that utilises a randomised unscented transformation which is a special case of stochastic integration rules providing an unbiased estimate of an integral. The new filter provides estimates of higher quality than the traditional filters and renders a randomised version of the unscented Kalman filter. The proposed filter is illustrated in a numerical example.

Numerical Differentiation on Irregular Grids

04:00 PM Wednesday 31, 1969

In this article, we propose a multidimensional numerical differentiation method from irregularly sampled data, in a noisy environment. The method extends to irregular grids our previous work and it relies on the same spirit as the algebraic numerical differentiators due to M. Mboup et al. (Numerical differentiation with annihilators in noisy environment, Numerical Algorithm, 50, pp. 439-457, 2009). We provide a least squares interpretation of the developed estimators as well as a discrete implementation scheme. Several numerical simulations are presented to asses the performance of the proposed differentiators.

Risk-Sensitive Cubature Filtering for Jump Markov Nonlinear Systems and Its Application to Land Vehicle Positioning

04:00 PM Wednesday 31, 1969

In this paper, a risk-sensitive filter for a class of jump Markov nonlinear systems is proposed. By using a set of weighted cubature points to approximate the intractable risk-sensitive recursions, the proposed filter could exhibit improved numerical stability with respect to the derivation of the square-root covariance, for which the unscented transform technique might halt the operations due to the presence of non-positive definite covariance. The performance of the proposed filter is illustrated through a simulation study of tracking a land vehicle with maneuvers.

A New Paradigm for State Estimation in Nonlinear Systems Via Minimum Distortion Filtering

04:00 PM Wednesday 31, 1969

It is well know that, for linear gaussian processes, the Kalman Filter provides an elegant solution to the recursive state estimation problem. However, when the process is nonlinear, then one needs to use various approximations to the filtering problem. In this paper we describe a new approach to nonlinear filtering based onMinimumDistortion Filtering. At the core of this algorithmis a deterministic on-line griding technique based on Vector Quantization. We explore several practical issues associated with the algorithmwhich are necessary to ensure that it runs effectively.We also present several examples which illustrate the utility of this class of algorithm in the context of nonlinear state estimation.

A Novel Technique Based on Up-Sampling for Addressing Modeling Issues in Sampled Data Nonlinear Filtering

04:00 PM Wednesday 31, 1969

We address sampled data non-linear filtering problems where there is an underlying continuous-time system. In the case of linear systems, it is well known that there is an exact discrete model that describes the second order properties at the sampling instants. However, in the nonlinear case, one must use an approximate model. In practice, simple Euler expansions are typically used. However, an Euler model is known to give a poor approximation especially with moderate sample period. Here we propose a resolution of this difficulty via the use of an up-sampling strategy. We show that, as the up-sampling rate increases, then in the linear case the up-sampled filter converges to the true filter. We illustrate by an example.

Adaptivity: A Quality Goal for Agent-Oriented Models?

04:00 PM Wednesday 31, 1969

A challenge for engineers is how to design systems that work effectively in todays complicated world. Five key characteristics of modern computing environments that need to be taken into account when building systems are: complexity, their distributed nature, time-sensitivity of information, the uncertainty and unpredictability of the surrounding environment, and its open nature new things happen. This is sometimes summarised as systems being dynamic. A desirable attribute for software within a dynamic system is adaptivity. As the world changes, our software ideally should evolve to reflect the change. As new facts enter the world, the software should not break. An obvious area where adaptivity is essential is security. As a new virus or security threat is determined, it would be good if the virus checking/firewall/security system incorporated a response to the new threat automatically. How do the system know how to adapt in response to new events and situations? There has to be some purposefulness that the system can refer to. An additional attribute that I strongly advocate is that the software should be understandable in its design and purpose. We need ways of thinking about and describing software which simplifies complexity, at least in regarding to describing behaviour.

Modified High-Order Adaptive Algorithm for Decentralized Control of Multi-Agent Structurally Uncertain Plants under Disturbance

04:00 PM Wednesday 31, 1969

The subject of this paper is solving the adaptive dynamic controller design problem for multi-agent systems with structural and parametric uncertainty for the case when derivatives of input and output parameters cannot be measured. The operability of the designed control systems subject to non-measurable bounded disturbances is presented. Only the measurable variables of the local subsystems are used to generate the control actions, therefore control is completely decentralized.

Hybrid Automata Dicretising Agents for Formal Modelling of Robots

04:00 PM Wednesday 31, 1969

Some of the fundamental capabilities required by autonomous vehicles and systems for their intelligent decision making are: modelling of the environment and forming data abstractions for symbolic, logic based reasoning. The paper formulates a discrete agent framework that abstracts and controls a hybrid system that is a composition of hybrid automata modelled continuous individual processes. Theoretical foundations are laid down for a class of general model composition agents (MCAs) with an advanced subclass of rational physical agents (RPAs). We define MCAs as the most basic structures for the description of complex autonomous robotic systems. The RPAs have logic based decision making that is obtained by an extension of the hybrid systems concepts using a set of abstractions. The theory presented helps the creation of robots with reliable performance and safe operation in their environment. The paper emphasizes the abstraction aspects of the overall hybrid system that emerges from parallel composition of sets of RPAs and MCAs.

Designing Adaptive Multi-Agent Systems by Agent-Oriented Modelling

04:00 PM Wednesday 31, 1969

The challenges in creating software for modern complex and distributed computing environments are time-sensitivity, uncertainty, unpredictability, and openness. It is a problem how to design systems that work effectively in the modern environment, where computing is pervasive, people interact with technology existing in a variety of networks, and under a range of policies and constraints imposed by the institutions and social structures that we live in. The key concepts we use for designing open, adaptive, distributed, and self-managing systems are agents and sociotechnical systems. An agent is suitable as a central modelling abstraction for representing distributed interconnected nodes of the modern world. A sociotechnical system encompasses a combination of people and computers, hardware and software, many of which can be viewed as agents. This article addresses the bottom-up development of sociotechnical systems as adaptive multi-agent systems. We claim that the methods for designing adaptive multi-agent systems should be borrowed from social sciences rather than from exact sciences. In particular, we propose a solution for developing flexible multi-agent systems in such a way that an environment does not have to be analysed in all its complexity.

Decision Methods for Non-Tethered Deep Space Interferometry

04:00 PM Wednesday 31, 1969

This paper examines decision methods applied to a distributed system that must operate collaboratively to achieve a common objective and tolerate partial system failure, necessitating structural reorganization. The problem addressed is controlled and cooperative action of multiple physical agents in a space environment, tasked with forming an interferometer, maximizing the interferometer lifetime by staged placement of resources and maintaining optimality in the presence of individual agent failures. Whilst a seemingly niche application, the methods developed and analyzed are equally valid for any multiplephysical agent system such as UAVs or AUVs. Centralized optimization methods will be applied to form decisions in addition to a distributed contract-net like decision method, wherein an auction system is adopted to form group decisions. These methods are investigated for the practicality of applying such methods to an engineering system.

Optimal Control of a Class of Networked Systems Based on MLD Framework

04:00 PM Wednesday 31, 1969

A networked control system (NCS) is a control system in which plants, sensors, controllers, and actuators are connected through communication networks. In this paper, as one of the design problems for NCSs, we consider optimal sampled-data control of linear systems with uncertain input delay and uncertain sampling period. First, an input delay system is transformed into a discrete-time system with parameter uncertainty. Furthermore, the obtained system is expressed as a mixed logical dynamical model by using our previously proposed modeling method. Next, a given continuous-time cost function is transformed into a discrete-time cost function with parameter uncertainty, and the optimal control problem is approximately expressed as a mixed integer programming problem.

LQG Control for Networked Control Systems with Random Packet Delays and Dropouts Via Multiple Predictive-Input Control Packets

04:00 PM Wednesday 31, 1969

This article addresses the Linear Quadratic Gaussian (LQG) optimal control problem for networked control systems when data is transmitted through a TCP-like network and both measurement and control packets are subject to random transmission delays and packet dropouts. Instead of adopting a zero-input or hold-input strategy, we propose a predictive optimal-input strategy, where at each time instant, K future control inputs are computed and sent in addition to the current one in the same control packet. The stabilizability conditions of the system are then derived. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Robust Dissipative Control for Networked Control Systems with Multiple Packet Dropouts

04:00 PM Wednesday 31, 1969

This paper deals with the dissipative problem for uncertain time-delay networked control systems with both multiple measurement and control packet dropouts. The uncertainty is assumed to satisfy a dissipative inequality, and the multiple measurement and control packet dropouts are described by two independent Bernoulli distributed sequences. By utilizing the Lyapunov functional method, a robust dissipative controller is designed such that the corresponding closed-loop system is asymptotically mean-square stable and strict~$(Q, S, R)$-dissipative. The sufficient condition on the existence of the controller is formulated in the form of linear matrix inequalities. Then the controller gain is achieved by using an extended cone complementarity linearization method. An example is given to illustrate the effectiveness of the proposed design method.

Sparse Representations for Packetized Predictive Networked Control

04:00 PM Wednesday 31, 1969

We investigate a networked control architecture for LTI plant models with a scalar input. Communication from controller to actuator is over an unreliable network which introduces packet dropouts. To achieve robustness against dropouts, we adopt a packetized predictive control paradigm wherein each control packet transmitted contains tentative future plant input values. The novelty of our approach is that we seek that the control packets transmitted be sparse. For that purpose, we adapt tools from the area of compressed sensing and propose to design the control packets via on-line minimization of a suitable l¹/l² cost function. We then show how to choose parameters of the cost function to ensure that the resultant closed loop system be practically stable, provided the maximum number of consecutive packet dropouts is bounded. A numerical example illustrates that sparsity reduces bit-rates, thereby making our proposal suited to control over unreliable and bit-rate limited networks.

A Decoupled Feedback Structure for Covertly Appropriating Networked Control Systems

04:00 PM Wednesday 31, 1969

The use of a communication network in the transmission of control system signals (measurements and actuation) is becoming more widespread. If the communication (or the sensors and actuators themselves) can be modified by a malicious agent then the control of the physical plant can be covertly appropriated. A parameterised decoupling structure is introduced which allows the covert agent a wide range of control actions on the physical plant while remaining undetectable from the point of view of the original networked controller. The designer of the covert agent need only have a model of the physical plant; knowledge of the networked controller is not required. A MIMO process control example (based on the control of irrigation canals) is used to illustrate the concepts.

Simple Conditions for $L_2$ Stability and Stabilization of Networked Control Systems

04:00 PM Wednesday 31, 1969

The stability analysis and stabilization of networked control systems subject to data loss and time-varying transmission delays are explored. The stability result is based on quadratic separation and operator theory, which allows to capture the above phenomena into the single formalism of aperiodic sampling. The obtained stability condition is expressed through an LMI. The stabilization problem is a bit more involved due to the inherent structure of the obtained LMI. An approximation (dilation) is then proposed to obtain a more tractable LMI for stabilization. Several examples illustrate the effectiveness of the proposed approach.

Discrete-Time Adaptive Mixing Control with Stability-Preserving Interpolation: The Output Regulation Problem

04:00 PM Wednesday 31, 1969

The main result of this paper is the extension of the Adaptive Mixing Control (AMC) approach, to the discrete-time setting. The stability and robustness properties of the adaptive mixing control scheme are analyzed. It is shown that in the ideal case, when no disturbances or unmodelled dynamics are present, the tracking error converges to zero; otherwise the mean-square tracking error is of the order of the modeling error provided the unmodelled dynamics satisfy a norm-bound condition. A stability preserving method for the synthesis of the multicontroller is also proposed, by interpolating a family of candidate controllers. A two carts system is used to show, via simulations, the effectiveness of the method.

Fast Extremum-Seeking for Hammerstein Plants

04:00 PM Wednesday 31, 1969

The prevailing analyses of sinusoidally perturbed extremum-seeking (ES) schemes require the ES scheme to act slowly relative to the plant dynamics. Existing analyses that do allow for fast ES are fairly restrictive, considering only local behaviour on Wiener--Hammerstein plants where the nonlinear element is quadratic. In this paper, semi-global stability of an ES scheme acting on a general Hammerstein plant is considered. A simple tuning approach is presented, allowing the ES scheme to achieve arbitrarily fast convergence of the plant input from an arbitrarily large set of initial conditions to an arbitrarily small neighbourhood of the value that minimises (or maximises) the plant output.

Gain Selection in Observer-Based Extremum Seeking Schemes

04:00 PM Wednesday 31, 1969

Traditionally, sinusoidally perturbed extremum seeking (ES) schemes utilise a gradient descent adaptation law to update the mean control input toward the optimising set point. The tuneable gain, k, in this adaptation law must be chosen sufficiently small to guarantee convergence but as large as possible to ensure fast convergence. However, previous analyses are unable to explicitly provide the upper bound on k guaranteeing convergence. Here, an observer based ES approach is used within a particular ES framework for a static plant. Deviating from the classical sinusoidally perturbed ES approach, specific plant information is assumed to be available and this results in an analytical estimate of the upper bound on k for non-local stability. The conservativeness of this estimate is investigated in simulations.

A Constructive Procedure Based on Dynamic Scaling for Adaptive Control of Nonlinearly Parameterized Nonlinear Systems

04:00 PM Wednesday 31, 1969

A new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized, nonlinear systems was recently proposed by the authors. The key step is the construction of a monotone mapping, via a suitable selection of a controller tuning function, which has to satisfy some integrability conditions this translates into the need to solve a partial differential equation (PDE). In this paper this result is extended providing some answers to the questions of characterization of monotonizable systems and solvability of the PDE. First, adding to the design a nonlinear dynamic scaling, we obviate the need to solve the PDE. Second, for the case of factorizable nonlinearities, the following results are established. (i) It is shown that the monotonicity condition is satisfied if a linear matrix inequality is feasible. (ii) Directly verifiable involutivity conditions that ensure the solution of the PDE are presented. (iii) An explicit formula for the required tuning function is given, provided the regressor matrix satisfies some rank conditions. Hence, adding a dynamic scaling, this yields a constructive solution to the problem.

Model-Free Prescribed Performance Control

04:00 PM Wednesday 31, 1969

A universal controller is designed for strict feedback systems with unknown nonlinearities, capable of guaranteeing, for any a priori known initial state condition, bounded signals in the closed loop, as well as prescribed performance for the output tracking error. By prescribed performance we mean that the output tracking error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, exhibiting maximum overshoot less than some sufficiently small preassigned constant. The proposed control scheme is of low complexity and requires reduced levels of a priori system knowledge. A comparative simulation study verifies the superiority of the proposed control scheme against the well known backstepping technique, which has been the main tool for designing controllers for the class of systems considered.

Adaptive Suboptimal Regulation of Input Constrained Plants with Bounded Disturbances

04:00 PM Wednesday 31, 1969

This paper deals with adaptive regulation of a discrete-time linear time-invariant plant with arbitrary bounded disturbances whose control input is constrained to lie within certain limits. The adaptive control algorithm exploits the one-step-ahead control strategy and the gradient projection type estimation procedure using the modified dead zone. The sufficient conditions guaranteeing the global asymptotical stability and simultaneously the suboptimality of the closed-loop systems are derived. Numerical exam-ples and simulations are presented to support the theoretical results.

Predictive Control for Tight Group Formation of Multi-Agent Systems

04:00 PM Wednesday 31, 1969

This paper addresses the real-time control problem of a group of agents in the presence of non-convex collision avoidance constraints. The goal is to guarantee the convergence towards a tight formation. Convex (polyhedral) regions will be used to define safety regions around each agent. Then, using the dynamics and constraints, an optimization-based control design can be adopted upon an appropriate receding horizon principle. A single optimal control problem is solved based on a prediction of the future evolution of the system and the resulting control law is implemented in a centralized way. At the supervision level, it is shown that the decision about which agents should take on what role in the desired tight formation is equivalent with a classical pairing (or task assignment) problem. An important contribution is the re-evaluation of the pairing at each iteration.

A System Theory Proof of the Infeasibility of Entanglement Generation in Gaussian Quantum Systems Via Classical Control

04:00 PM Wednesday 31, 1969

This paper uses a system theoretic approach to show that classical linear time invariant controllers cannot generate steady state entanglement in a bipartite Gaussian quantum system which is initialized in a Gaussian state. The paper also shows that the use of such controllers cannot generate entanglement in a finite time from a bipartite system initialized in a separable Gaussian state. The approach reveals connections between systems theoretic concepts and the well known physical principle that local operations and classical communications cannot generate entangled states starting from separable states.