Time-varying Polytopic Uncertainties Research Articles

Adaptive Augmenting Control Design for Time-Varying Polytopic Systems

To increase the performance of closed-loop controlled systems in off-nominal conditions and in the presence of inevitable faults and uncertainties, a systematic approach based on robust convex optimization for adaptive augmenting control design is discussed in this paper. More specifically, this paper addresses the problem of adaptive augmenting controller (AAC) design for systems with time-varying polytopic uncertainty. First, a robust state-feedback controller is designed via robust convex optimization as a baseline controller. The closed-loop polytopic system with the baseline controller is considered as the desired time-varying reference model for the design of a direct state-feedback adaptive controller. Next using Lyapunov arguments, global stability of combined robust baseline and adaptive augmenting controllers is established. Furthermore, it is proved that tracking error converges to zero asymptotically. A case study for a generic nonminimum phase nonlinear pitch-axis missile autopilot is conducted. Simulation tests are performed to evaluate stability and performance of nonlinear time-varying closed-loop system in the presence of uncertainties in pitching moment and normal force coefficients, and unmodeled time delays. In addition, results of the simulations indicate satisfactory robustness in case of severe loss of control effectiveness event.

Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs

Summary This paper is concerned with the problem of reachable set estimation (RSE) for linear systems with time-varying delays and bounded peak inputs. The purpose is to find an ellipsoid that contains the system state in presence of all bounded peak inputs. First, the RSE problem for nominal time-delay systems is studied based on a relaxed Lyapunov–Krasovskii functional which does not require all the involved symmetric matrices to be positive definite. Delay-dependent and delay-rate-dependent conditions for the existence of a desired ellipsoid are obtained. Second, the RSE problem for time-delay systems with time-varying polytopic uncertainties is investigated. Under the assumption that the uncertain parameters are differentiable and their derivatives are bounded by known scalars, parameter-rate-dependent conditions for the existence of a desired ellipsoid are derived by using a parameter-dependent Lyapunov–Krasovskii functional. When the differentiability of the uncertain parameters is not taken into account, a common Lyapunov–Krasovskii functional is employed to tackle the addressed problem, and parameter-rate-independent conditions are presented. All the obtained conditions are given in terms of matrix inequalities, which become linear matrix inequalities when only one non-convex scalar is prescribed. Finally, the reduced conservatism of the obtained results in comparison with recent ones in the literature is shown through numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Finite-time boundedness analysis for a new multi-layer switched system with time-delay

In this paper, the finite-time boundedness problem of a multi-layer switched system subject to average dwell time switching signal, Markov jump and time-varying polytopic uncertainties is investigated. The sufficient conditions guaranteed the conclusion are shown in the form of linear matrix inequalities to ease the formulation, and the switched Lyapunov–Krasovskii approach is used in detail proofs. At last, an illustrative example is employed to demonstrate the efficiency of the main result.

A New Fault Detection Scheme for Networked Control Systems Subject to Uncertain Time-Varying Delay

Fault detection of networked control systems (NCS) subject to uncertain time-varying delay is studied in this paper. For the convenience of residual generator design, influence caused by network-induced delay is first transformed into time-varying polytopic uncertainty, which greatly facilitates further manipulation. Then design of the optimal residual generator is formulated as a model matching problem, i.e., to design a residual generator best matching the optimal residual generator of NCS in the delay free case. This procedure is assisted by parameter-dependent Lyapunov function matrix based bounded real lemma, which has been proved to be much better than single constant Lyapunov function matrix based results. This approach not only can be used in conditions that the variation part of the delay is less than one sampling period, but also can be applied to scenarios where the variation part of the delay is larger than one sampling period. Simulation results are also given to illustrate effectiveness of the proposed method.

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H 2 and H ∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

Simplified adaptive control via improved robust positive real conditions

A new method is derived for embedding plants in a robust state-feedback scheme, to achieve strictly positive realness of the resulting augmented plants. A state-feedback gain is derived that guarantees the strictly positive realness of the closed-loop in presence of polytopic type, possibly time-varying, parameter uncertainties in the model that describes the plant. This is achieved by assigning different Lyapunov functions to each of the vertices of the uncertainty polytope. The obtained feedback gain is used to apply existing methods for robust simplified adaptive control on systems with possibly time-varying polytopic uncertainties.