Static Output Feedback Model Predictive Control for Uncertain Linear Systems

A stabilizing output feedback model predictive control algorithm is proposed for linear systems with input constraints. Dual mode control strategy is adopted: the state observer, linear feedback controller and terminal constraint set are pre-computed; if the state is contained in terminal constraint set, linear feedback controller is used; otherwise a linear control structure with free vector is used, and control law can be obtained by solving an Second Order Cone Programming (SOCP) problem. The system with bounded disturbance is considered and bounded stability is shown. Simulations results show the effectiveness of the control algorithm.

An LMI-Based Approach to Static Output Feedback Stabilization of T—S Fuzzy Systems

Static output feedback controller design for fuzzy systems: An ILMI approach

This paper presents dynamic output feedback model predictive control (DOFMPC) for nonlinear systems represented by a Hammerstein–Wiener model. Compared with a previous work (IET-OFMPC: output feedback model predictive control for nonlinear systems represented by Hammerstein–Wiener model. IET Control Theory & Applications, 2007, 1 (5) pp. 1302–1310), this paper uses the notion of quadratic boundedness to specify the closed-loop stability and guarantees the recursive feasibility of the optimization problems. By optimizing all the parameters of the dynamic output feedback law within a single optimization problem, the computational burden is very huge. Hence, an alternative formulation is also proposed with much lower on-line computational burden. Numerical examples are given to illustrate the effectiveness of the controllers.

ROBUST NETWORKED OUTPUT FEEDBACK PREDICTIVE CONTROLLER DESIGN

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

SummaryIn this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

A state space linear mathematical model oriented to the design of Passive and Active Mass Dampers for tall buildings and bridges in wind is presented. The model accounts for an arbitrary number of passive and active devices located at arbitrary points of the structure. The aerodynamic terms of the stiffness and damping matrices are considered in order to reproduce the behavior of the structure under the wind excitation. A general discussion on the application of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> techniques to the synthesis of the active control law is carried out. For the tuning of the mechanical parameters of the devices, the problem is reformulated as a decentralized static output feedback control law design problem.

Stabilization of fractional-order singular uncertain systems

Robust fault-tolerant control for networked control systems subject to random delays via static-output feedback

By complementarily fusing the robust stabilizability condition, the orthogonal-functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is proposed in this paper to design the robust-stable and quadratic-optimal static output feedback controller such that i) the linear singular control system with structured parameter uncertainties is regular, impulse-free and asymptotically stable and ii) a quadratic finite-horizon integral performance index for the linear nominal singular control system can be minimized. Based on some essential properties of matrix measures, a new sufficient condition is presented for ensuring that the linear singular system with structured and quadratically-coupled structured parameter uncertainties is regular, impulse free and asymptotically stable. By using the OFA and the robust stabilizability condition, the dynamic-optimization problem for the robust-stable and quadratic-optimal static output feedback control design of the linear uncertain singular system is transformed into a static-constrained-optimization problem represented by the algebraic equations with constraint of robust stabilizability condition; thus greatly simplifying the robust-stable and quadratic-optimal static output feedback control design problem of the linear uncertain singular system. Then, for the static-constrained-optimization problem, the HTGA is employed to find the robust-stable and quadratic-optimal static output feedback controller of the linear uncertain singular control system. One design example of the robust-stable and quadratic-optimal static output feedback controller for a mass-spring-damper mechanical system with structured parameter uncertainties is given to demonstrate the applicability of the proposed integrative approach.

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov—Krasovskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method.

Particle Swarm Optimization for the design of H∞ static output feedbacks

A linear control system defined by a stationary differential equation of nth order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.

We design a Lyapunov based-boundary feedback controller for achieving mixing in a three-dimensional (3-D) pipe flow governed by Navier-Stokes equations. We show that the control law maximizes a measure related to mixing (that incorporates stretching and folding of material elements), while at the same time minimizing the control effort and the sensing effort. The penalty on sensing results in a static output-feedback control law (rather than full-state feedback). We also derive a lower bound on the gain from the control effort to the mixing measure. Furthermore, we establish input-output-to-state-stability properties for the open-loop system. These results show a form of detectability of mixing in the interior of the pipe from the chosen outputs on the wall. The effectiveness of the optimal control in achieving mixing enhancement is demonstrated in numerical simulations.