Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

Piecewise Linear Control Systems

This thesis treats analysis and design of piecewise linear control systems. Piecewise linear systems capture many of the most common nonlinearities in engineering systems, and they can also be used for approximation of other nonlinear systems. Several aspects of linear systems with quadratic constraints are generalized to piecewise linear systems with piecewise quadratic constraints. It is shown how uncertainty models for linear systems can be extended to piecewise linear systems, and how these extensions give insight into the classical trade-offs between fidelity and complexity of a model. Stability of piecewise linear systems is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. The computations are based on a compact parameterization of continuous piecewise quadratic functions and conditional analysis using the S-procedure. A unifying framework for computation of a variety of Lyapunov functions via convex optimization is established based on this parameterization. Systems with attractive sliding modes and systems with bounded regions of attraction are also treated. Dissipativity analysis and optimal control problems with piecewise quadratic cost functions are solved via convex optimization. The basic results are extended to fuzzy systems, hybrid systems and smooth nonlinear systems. It is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization. An automated procedure for increasing the flexibility of the Lyapunov function candidate is suggested based on linear programming duality. A Matlab toolbox that implements several of the results derived in the thesis is presented

Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance

[EN] Given a Takagi-Sugeno (TS) system, this paper proposes a novel methodology to obtain the state feedback controller guaranteeing, asymptotically as a Polya-related complexity parameter grows, the largest (membership-shape independent) possible domain-of-attraction with contraction-rate performance lambda, based on polyhedral lambda-contractive sets from constrained linear systems literature. The resulting controller is valid for any realisation of the memberships, as usual in most TS literature. For a finite complexity parameter, an inner estimate of such largest set is obtained; the frontier of such approximation can be understood as the level set of a polyhedral control-Lyapunov function. Convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for TS system stabilisation: for a high-enough value of the complexity parameter, any conceivable shape-independent Lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm's output. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by grants DPI2015-70433- P and DPI2016-81002-R, from Spanish Government (MINECO) and grant PROMETEOII/2013/004 from Generalitat Valenciana.Ariño-Latorre, CV.; Sala, A.; Pérez Soler, E.; Bedate Boluda, F.; Querol-Ferrer, A. (2017). Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance. Fuzzy Sets and Systems. 316:117-138. https://doi.org/10.1016/j.fss.2016.10.004S11713831

Rapid-convergent nonlinear differentiator

A nonlinear differentiator being fit for rapid convergence is presented, which is based on singular perturbation technique. The differentiator design can not only sufficiently reduce the chattering phenomenon of derivative estimation by introducing a continuous power function, but the dynamical performances are also improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating nonlinear items and the linear filter. The merits of the rapid-convergent differentiator include the excellent dynamical performances, restraining noises sufficiently, avoiding the chattering phenomenon and being not based on system model. The theoretical results are confirmed by computer simulations and an experiment.Comment: 26 pages, 15 figure