A SOS-based approach to residual generators for discrete-time polynomial nonlinear systems

Nonlinear matrix inequality approach based heading control for an autonomous underwater vehicle with experimental realization

Observer-based control for time-delayed quasi-one-sided Lipschitz nonlinear systems under input saturation

In this note, we deal with the stability and stabilization problems for nonlinear quadratic discrete-time periodic systems. By using the quadratic Lyapunov function, and a so called periodic invariant set, delay-independent sufficient conditions for local stability and local stabilization for nonlinear quadratic discrete-time periodic systems are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

The methods of frozen Riccati equations and nonlinear matrix inequalities (NLMIs) offer certain computational advantages over Hamilton-Jacobi equations (HJE), but may fail to be optimal. The frozen Riccati method uses a non-unique state-dependent linear representation to reduce the HJE to a state-dependent Riccati equation. While there usually exists some choices that recover the optimality, it may be difficult to find. The NLMI computation for analysis and synthesis is shown to be as hard as Lyapunov stability analysis; a finite difference approximation scheme is proposed to solve the NLMIs.

The stability and performance robustness analysis for a class of uncertain nonlinear systems with bounded structured uncertainties are characterized in terms of various types of nonlinear matrix inequalities (NLMIs). As in the linear case, scalings or multipliers are used to find Lyapunov functions that give sufficient conditions, and the resulting NLMIs yield convex feasibility problem. For these problems, robustness analysis is essentially no harder than stability analysis of the system with no uncertainty. Sufficient conditions for the solvability of related robust synthesis problems are developed in terms of NLMIs as well. >

A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of nonlinear systems subject to L/sub 2/-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem. As in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the solvability of robustness synthesis problems are represented in terms of NLMIs as well. With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favourable.

Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input

Exponential stabilizability and robustness analysis for discrete-time nonlinear systems

The package NLControl, developed in the Institute of Cybernetics at Tallinn University of Technology within the Mathematica environment, has been made partially available over the internet using webMathematica tools. The package consists of functions that assist the solution of different modelling, analysis, and synthesis problems for nonlinear control systems, described either by state or by input-output equations. This paper focuses on describing the webMathematica-based tools for discrete-time nonlinear control systems.

This paper investigates the formation control problem of heterogeneous discrete-time nonlinear multi-agent systems with structural uncertainties. The control objective is to make the outputs of agents reach a desired formation while tracking a leader. The formation control problem of heterogeneous discrete-time multi-agent systems is first converted into a robust output regulation problem, and then, a distributed formation control scheme based on output regulation framework is proposed. A $p$ -copy internal model is synthesized into the distributed formation control law such that the overall closed-loop system can be robust to structural uncertainties. It is shown that the heterogeneous discrete-time nonlinear multi-agent system can reach the desired formation regardless of small parameter permutations of agents under the proposed control law. Finally, simulation and experiment studies are provided to demonstrate the effectiveness of the proposed control law.

Prescribed performance based data-driven adaptive sliding mode control for discrete-time nonlinear systems

In this thesis a certain estimation problem for nonlinear stochastic dynamical systems in discrete time, known as filtering in the literature, is considered. The objective is to reconstruct the current state of the system by means of observations. The observations are noise corrupted measurements of a function of the state.In the first chapter we will provide concepts from probability theory necessary to define and investigate the nonlinear filtering problem. The definition of the nonlinear filter is presented in the second section of this chapter.The second chapter explains in detail why filtering is an extremely difficult problem in a nonlinear context. It turns out that a finite dimensional representation of the filter is possible in very special circumstances, only. This chapter summarizes known results and is intended mainly as a motivation for the necessity of investigating approximation schemes for the nonlinear filter, considered in the following two chapters.Numerical approximation methods are then investigated from a general point of view in the third chapter. A general framework to obtain error bounds for approximation schemes is presented. Necessary for this investigation are metrics for probability distributions we will make extensive use of. Furthermore, an essential property of the filter required to give a bounded approximation error turns out to be a negative Lyapunov exponent of the filter dynamics.The fourth chapter provides some classes of approximation methods. Common to all these methods are projection techniques on parametrized families of probability distributions. This approach was carried out for continuous time systems already by several authors. However, the error analysis carried out in this thesis is, to the best of our knowledge, new.The last two chapters present (aside from two small sections devoted to a Monte Carlo approach), two interesting and important applications of nonlinear filtering. The first is estimation of an unknown parameter in the dynamics. This problem is very important in all branches of science, and we will present two numerical examples. The second application is reconstruction of a sent message in telecommunications. To this problem a chapter is devoted, including results on the bit error probability obtained using methods from nonlinear filtering theory for a simple transmitter model.To summarize, the aim of this thesis is threefold. First, to show that filtering of nonlinear dynamical system is a nontrivial and interesting problem from a mathematical point of view, second to show methods to overcome the difficulties arising in applications, and third to show that filtering is not a purely artificial mathematical problem but has a great significance in science and engineering.

In this paper, a novel on-line value iteration (VI) adaptive (or approximate) dynamic programming (ADP) is developed to solve the optimal control problems for nonlinear discrete-time affine systems, which updated the value function and policy function at the each step running of the system. The critical point of this algorithm is to combine local VI-ADP algorithm with gaussian distribution regarded the current states as the expected. Moreover, for implementing the on-line VI-ADP algorithm, the actor-critic structure composed of the neural networks realizes the value function and the strategy function. In addition, the model neural network enables the algorithm to replace the system dynamics in a data-driven way, that is, without of the system dynamic knowledge is feasible. Finally, simulations show that this on-line VI-ADP algorithm can solve the regulation and tracking problems effectively.

This manuscript deals with parametric and state estimation problem of discrete-time nonlinear polynomials systems. In this respect, the aim is to design a Recursive State and Parametric Estimation (RSPE) algorithm, based on least square principle, polynomial adjustable models and Kalman filter theory. Our simulation results show the validity of the proposed algorithm.

A REFERENCE MODEL BASED ROBUST ℋ∞ FILTERING APPROACH TO FAULT DETECTION IN UNCERTAIN SYSTEMS