Convex reformulations for self-optimizing control optimization problem: Linear Matrix Inequality approach

An improved model-free adaptive control for nonlinear systems: An LMI approach

Preface Notation Part I. Introduction. Robust Decision Problems in Engineering: A linear matrix inequality approach L. El Ghaoui and S.-I. Niculescu Part II. Algorithms and Software: Mixed Semidefinite-Quadratic-Linear Programs J.-P. A. Haeberly, M. V. Nayakkankuppam and M. L. Overton Nonsmooth algorithms to solve semidefinite programs C. Lemarechal and F. Oustry sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure S.-P. Wu and S. Boyd Part III. Analysis: Parametric Lyapunov Functions for Uncertain Systems: The Multiplier Approach M. Fu and S. Dasgupta Optimization of Integral Quadratic Constraints U. Jonsson and A. Rantzer Linear Matrix Inequality Methods for Robust H2 Analysis: A Survey with Comparisons F. Paganini and E. Feron Part IV. Synthesis. Robust H2 Control K. Y. Yang, S. R. Hall and E. Feron Linear Matrix Inequality Approach to the Design of Robust H2 Filters C. E. de Souza and A. Trofino Robust Mixed Control and Linear Parameter-Varying Control with Full Block Scalings C. W. Scherer Advanced Gain-Scheduling Techniques for Uncertain Systems P. Apkarian and R. J. Adams Control Synthesis for Well-Posedness of Feedback Systems T. Iwasaki Part V. Nonconvex Problems. Alternating Projection Algorithms for Linear Matrix Inequalities Problems with Rank Constraints K. M. Grigoriadis and E. B. Beran Bilinearity and Complementarity in Robust Control M. Mesbahi, M. G. Safonov and G. P. Papavassilopoulos Part VI. Applications:Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization J. Oishi and V. Balakrishnan Multiobjective Robust Control Toolbox for LMI-Based Control S. Dussy Multiobjective Control for Robot Telemanipulators J. P. Folcher and C. Andriot Bibliography Index.

We propose a congestion control algorithm and design a state feedback controller for regulating the congestion of available bit rate (ABR) traffic in asynchronous transfer mode (ATM) networks. ABR service is specified as the rate-based feedback mechanism for congestion control and provides a control signal to throttled sources from a bottleneck node in order to adjust the throttled source rates based on available capacity. Our main purposes are as follows: (1) to design a state feedback controller; (2) to place the closed-loop poles in any desired regions based on a pole placement constraint; (3) to use the LMI (linear matrix inequalities) approach for finding the optimal state feedback gain K. The simulation results show that, under pole placement and LMI approaches, our state feedback congestion controller for ABR traffic in ATM networks can possibly guarantee the system stability, provide no buffer overflow, determine the optimal source traffic rates and place the closed-loop poles in any desired regions as well.

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of ℝ n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasiconvergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov-like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

This paper proposes the output feedback optimal guaranteed cost controller design method for uncertain piecewise linear systems based on the piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed‐loop augmented systems, the existence of the guaranteed cost controller for closed‐loop uncertain piecewise linear systems is cast as the feasibility of a set of bilinear matrix inequalities (BMIs). Some of the variables in BMIs are set to be searched by genetic algorithm (GA), then for a given chromosome corresponding to the variables in BMIs, the BMIs turn to be linear matrix inequalities (LMIs), and the corresponding non‐convex optimization problem, which minimizes the upper bound on cost function, reduces to a semidefinite programming (SDP) which is convex and can be solved numerically efficiently with the available software. Thus, the output feedback optimal guaranteed cost controller can be obtained by solving the non‐convex optimization problem using the mixed algorithm that combines GA and SDP. Numerical examples show the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

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.

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This paper proposes a new robust FIR equalizer for discrete time systems subject to parameter uncertainties in the matrices of the system state-space model from an H ∞ perspective. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The discrete algebraic Riccati inequality (DARI) and linear matrix inequality (LMI) provide an extremely superior methodology in the H ∞ control fields. By the H ∞ and robust methods in conjunction with the bounded real lemma, the robust FIR equalizer design is transformed into a standard LMI optimization problem. An example is given to illustrate the proposed methodology.

Non-synchronized Observer-based Control of Discrete-time Piecewise Affine Systems: an LMI Approach

Non-fragile observer-based controls of linear system via LMI approach

This paper is concerned with the problem of delay-derivative-dependent stability analysis for Markovian jumping neutral-type interval time-varying delay systems with mixed delays. The first, based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality approach, a delay-range-dependent condition for neutral-type Markovian jumping systems (NMJSs) with time-varying delays is obtained, which can guarantee global asymptotical stability of these NMJSs. Unlike the previous methods, the upper bound of the discrete delay and neutral delay derivative is taken into consideration even if this upper bound is larger than or equal to $$1(\dot{h}(t)<1,\dot{\tau}(t)<1)$$ . It is proved that the obtained results are less conservative than the existing ones. In our result, the time-varying delays are only assumed to be bounded. This has undoubtedly extended its application range. To better handle the problem on stability for neutral control systems, in which time-varying delay was involved, a stability criterion with less conservatism was put forward. Moreover, because our results in this paper are all based on the linear matrix inequality (LMI) approach, we can utilize Matlab’s LMI Control Toolbox to verify the global stability of correlation systems conveniently. As far as we are aware, this paper seems to be the first to discuss stability problems for neutral-type Markovian jumping systems with delay-derivative-dependence and delay-range-dependence.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

Mixed H∞/Passivity controller design through LMI approach applicable for waterflooding optimization in the presence of geological uncertainty

In this paper, in terms of Matrix Hadamard product a new control model is proposed for regulating connection coefficients of the state variables of the systems. It combines the traditional feedback compensation and the direct regulations for the connections of system states. The solution of control law to stabilize the systems via the regulations of connection coefficients can be obtained via a bilinear matrix inequality (BMI) involved Hadamard product. Under a certain conditions, we translate the BMI into a linear matrix inequality (LMI). Finally, we present some algebraic results when the matrices A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> have some special characters.

The simultaneous static output feedback stabilization problem for a collection of discrete-time interval systems with time delays is considered. A sufficient condition for the existence of static output feedback simultaneously stabilizing controllers is obtained in terms of matrix spectral norms. It is shown that this considered problem is solvable if a corresponding matrix's spectral norm assignment problem is solvable. Furthermore, we also show that the matrix spectral norm assignment problem is equivalent to a bilinear matrix inequality (BMI) problem. We then derive a sufficient condition for the BMI problem and the condition is a linear matrix inequality (LMI) feasibility problem, which can be solved easily. Finally, an example is provided to demonstrate the effectiveness of the proposed methodology.