Multiobjective State-Feedback Control Design with Non-Common LMI Solutions: A Subspace Approach

LMI RELAXATIONS FOR HOMOGENEOUS POLYNOMIAL SOLUTIONS OF PARAMETER-DEPENDENT LMIS

The Independent Administrative Corporation Japan Agency for Marine-Earth Science and Technology (JAMSTEC) has been developing light-and-small autonomous underwater vehicles (AUV), named “Marine Robot Experimental 1” (“MR-X1”). In this paper, the motion control problem of “MR-X1” is considered. Since the dynamics of “MR-X1” depends upon its own speed, the problem in question becomes a non-linear control problem. A new controller design method using linear matrix inequalities (LMIs) is proposed in order to adapt the problem in question. The algorithm, which gives a solution of a linear matrix inequality (LMI), can adapt to solve numerous LMIs simultaneously. LMIs can be obtained by substituting several speeds into the dynamics of “MR-X1”. The proposed controller, which can be derived from the solution of LMIs, becomes a stabilizing controller for all substituted speeds.

This paper presents the problem of observer-based fuzzy H/sup /spl infin// control for a class of uncertain nonlinear systems with time-varying delayed systems on the basis of Takagi-Sugeno fuzzy model. First, we design a fuzzy observer such that destination error system is globally, exponentially stable. Next, we design a fuzzy H/sup /spl infin// controller such that the closed loop system is globally, exponentially stable and achieves L/sub 2/ gain performance. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation. A sufficient condition for the existence of robust fuzzy H/sup /spl infin// controllers and observers are given in terms of linear matrix inequalities (LMIs). The control gains can also be directly obtained from the LMI solutions.

ABSTRACTThe aim of this paper is to propose a novel adaptive observer‐based stabilizer for a class of uncertain nonlinear time‐delay systems subject to unmatched external disturbances. A terminal sliding mode controller based on an adaptive super‐twisting terminal sliding mode observer is developed by using the linear matrix inequality (LMI) technique. Under the proposed scheme, the closed‐loop system converges to origin in finite time as the matching condition is satisfied and converges to the uniform ultimate bound in the effects of unmatched external disturbances. The design of the observer and the stabilizer does not require the upper bound of uncertainties and external disturbances. The chattering phenomenon is eliminated. The observer and the stabilizer can be efficiently designed from the solutions of LMIs. Simulation results illustrate the effectiveness of the proposed control scheme.

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with γ-disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.

This paper deals with the problem of robust stability and strictly passive control for a class of uncertain descriptor systems with time-delay. By using Lyapunov method and linear matrix inequality technique, delay-dependent sufficient conditions for the robust stability and strict passivity of the system are derived. In terms of solutions of linear matrix inequalities, the strictly passive state feedback controller of descriptor system is presented by introducing a slack variable. Finally, a numerical example shows the effectiveness of the proposed method.

Consider a (D x D) symmetric matrix A whose entries are linear forms in Q[X1, ..., Xk] with coefficients of bit size ≤ τ. We provide an algorithm which decides the existence of rational solutions to the linear matrix inequality A ≥ 0 and outputs such a rational solution if it exists. This problem is of first importance: it can be used to compute algebraic certificates of positivity for multivariate polynomials. Our algorithm runs within (k≤)O(1)2O(min(k, D)D2)DO(D2) bit operations; the bit size of the output solution is dominated by τO(1)2O(\min(k, D)D2). These results are obtained by designing algorithmic variants of constructions introduced by Klep and Schweighofer. This leads to the best complexity bounds for deciding the existence of sums of squares with rational coefficients of a given polynomial. We have implemented the algorithm; it has been able to tackle Scheiderer's example of a multivariate polynomial that is a sum of squares over the reals but not over the rationals; providing the first computer validation of this counter-example to Sturmfels' conjecture.

This paper considers the state estimation problem for Markovian jumping genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays. In order to approximate the true concentrations of the mRNA and protein, the state estimator is designed using available measurement outputs. The GRNs are composed of N modes. The system switches from one mode to another according to a Markovian chain with known transition probabilities. Based on the Lyapunov functionals, including triple integral terms, some inequalities, and a time-varying delay partitioning approach, delay-dependent criteria which employ all upper bounds of time delays of each mode are obtained in terms of linear matrix inequalities (LMIs). This guarantees that the estimation error dynamics can be globally asymptotically stable from solutions of LMIs. Finally, a numerical example is presented to demonstrate the efficiency of the proposed estimation scheme.

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm.

In this paper we give a state space solution to the H_-/H_∞ fault detection (FD) problem for linear time invariant dynamic systems. An H_-/H_∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state space realization of the optimal filter in an observer form via the solution of Linear Matrix Inequalities (LMIs). A numerical example is given to illustrate the algorithm.

In this paper a method is proposed to design an anti-windup scheme for discrete time linear systems with input saturations and actuator additive failures. This method provides a fault tolerant system reconfiguration mechanism with a control law which compensates for the estimated actuator additive faults and maintains the overall system stability in spite of actuator saturations. The design approach is derived from the solution of linear matrix inequalities (LMI) to guarantee the stability regions. For that purpose the fault tolerant control method is based on a linear quadratic regulator (LQR) and a fault estimator for compensation purposes. This method was tested in realistic simulations with the software Carins (CNES) on a pressure and mass flow rate model of a cryogenic test bench cooling circuit.

This paper is concerned with the stability for a class of switched uncertain neutral systems. The uncertainty is assumed to be of structured linear fractional from which includes the norm bounded uncertainty as a special case. Based on the property of completeness of systems, by using an improved Lyapunov-Krasovskii functional, a switching rule for the asymptotical stability of this systems is designed from the solution of linear matrix inequalities(LMIs). A numerical example is given to illustrate effectiveness of the result.

In this paper, we tackle the problem of stabilizing singularly perturbed switched affine systems. Even though efficient control strategies based on the solution of Linear Matrix Inequalities (LMIs) have been presented in the switched affine systems literature, the presence of the small singular perturbation parameter may introduce numerical difficulties in the solution of these LMIs due to ill conditioning. Moreover, this parameter may be uncertain or its use in the control law may not be practical. Here, we propose an LMI-based control design strategy that avoids the conditioning issues and that also provides an estimation of the domain of attraction. Furthermore, the resulting controller does not depend on the singular perturbation parameter. The proposed method is illustrated on a numerical example.

Descriptor- and Non-Descriptor Controllers in H∞ Control of Descriptor Systems