A numerical technique for optimal output feedback using Pade approximations

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

This paper considers the problem of static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching. By the aid of switched quadratic Lyapunov functions combined with Finsler’s lemma, new sufficient conditions for SOF stabilization are obtained which guarantee a γ-performance of the closed-loop switched systems subject to input disturbances. The proposed method can work successfully in situations where the existing ones fail. Three examples are given to illustrate its effectiveness.

The following paper considers the problem of static output feedback for a linear, time invariant system. Starting from a geometric model a new algorithm for finding a linear feedback law is derived. The well known condition m + p - 1 ≥ n for generic pole placement given by Kimura [8] is improved using geometric arguments in linear spaces.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Robust static output feedback infinite horizon RMPC for linear uncertain systems

This work eonsiden the H, norm control of structural systems with collocated sensors and actuators using an analytical upper bound approach. A parametrization of the output feedback control gains that achieve a desired H, norm bound is obtained using an analytical solution of the Bounded Real Lemma. This approach is verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed and the simulations show a drop of -6 dB in the H, norm of the closed loop system. Experimental results verify the simulated results and demonstrate the effectiveness of this method. The proposed control methodology has obvious computational advantages compared to traditional H, control design methods, especially for lnrge scale systems. The control of structural systems with collocated sensors and actuators has been shown to provide great advantages from a stability, passivity, robustness and an implementation viewpoint. For example, collocated control can easily be achieved in a space structure when an attitude rate sensor is placed at the same point as a torque actuator.(l)(2) The actuator placement and sizing optimization for vibration sup pression of a collocated beam structure is discussed in Ref. (3).Collocation of sensors and actuators leads to symmetric transfer functions. Several other classes of engineering sys- tems, such as circuit systems, chemical reactors and power networks, can be modelled as systems with symmetric trans- fer functions. Stabilization, robustness, model reduction and control of such systems has been examined recently.(4)(5) The H, norm control of structural systems has attracted a lot of attention recently due to the interpretation of the H, norm in the frequency domain. In early work, D-K iteration method was used to design H, controllers for a non-collocated flexible shucture. Now state space H, control based on the standard Riccati equation approach or the linear matrix inequality (LMI) formulation is a well developed control synthesis tool. The optimal static state feedback and full-order dynamic output feedback H, con- trol synthesis problems can be solved using iterations on the corresponding Riccati solutions or via the computational solution of a convex LMI optimization problem.(7)(8) On the other hand, the static output feedback and the fixed-order dynamic output feedback H, control synthesis problems are difficult computational problems since they require the

A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers

This paper presents a two-dimensional (2D)-based approach to the problem of output feedback repetitive control for uncertain discrete-time systems. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then sufficient conditions for the existence of output feedback control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal output feedback control law by minimizing the upper bound of a given cost function. Compared with the commonly used 1D-based method, the proposed approach increases the degree of freedom of controller design by not only including in the scheme an output feedback gain but also a feed forward one which can be simultaneously solved using the 2D-based procedures presented in the paper. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

this paper investigates the problem of robust gain-scheduled static output feedback (SOF) controller for a class of uncertain linear parameter varying systems (LPVSs). An uncertain LPVS is described by an interconnection of a nominal LPVS which is solely dependent on the measurable parameters, and a block structured uncertainty. For designing a H∞ gain-scheduled SOF controller as well as performing the stability analysis, the proposed method uses integral quadratic constraints (IQCs) to derive the linear matrix inequalities (LMIs) without any constraints on nominal system matrices. The performance and effectiveness of the proposed method are demonstrated based on an example.

Minimal-norm static feedbacks using dissipative Hamiltonian matrices

In this paper we propose a novel distributed algorithm for cooperative output regulation in networks of agents with identical dynamics. Namely, each agent utilizes local and relative output information in order to synchronize its output to the reference trajectory provided by a single node in the network. Stability analysis is carried out by the means of small-gain theorem, and it is shown that control synthesis comes down to a <tex>$\mathcal{H}_{\infty}$</tex> static output feedback problem. Simulation results that verify the effectiveness of the proposed algorithm are provided.

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H2, and H∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

A sufficient condition for the delay-independent asymptotic stability of dynamic systems with time-varying delayed states based on the algebraic Riccati inequality and related stabilizing controllers via static output feedback are derived. Then the robust stabilizing controllers for structured uncertain dynamic systems with time-varying delayed states via static output feedback are discussed. Finally, it is also shown that the stabilizing controller design of a given uncertain delay system via dynamic output feedback is equivalent to that of an augmented uncertain delay system via static output feedback. A numerical example is given to demonstrate the effectiveness of the proposed method.

This paper proposes a new integrated design method to simultaneously optimize the coupled structural parameters and controllers of mechanical systems by combining decentralized control techniques and Riccati-based control theories. The proposed integrated design method aims at minimizing the closed-loop H2 norm from the disturbance to the system cost. In this paper, the integrated design problems have been formulated in the cases of full state-feedback controllers and full order output-feedback controllers. We extend the current linear time invariant (LTI) control system to a more general framework suitable for the needs of integrated design, where the structural design is treated as a passive control optimization tackled by decentralized control techniques with static output feedback, while the active controller is optimized by solving modified Riccati equations. By using this dual-loop control system framework, the original integrated design problem is transferred to a constrained structural design problem with some additional Riccati-equation based constraints simultaneously integrating the controller synthesis. This reduces the independent design variables from the structural design parameters and the parameters of the controller to the structural design parameters only. As a result, the optimization efficiency is significantly improved. Then the constrained structural design problem is reformed as an unconstrained optimization problem by introducing Lagrange multipliers and a Lagrange function. The corresponding optimal conditions for the integrated design are also derived, which can be efficiently solved by gradient-based optimization algorithms. Later, two design examples, an active–passive vehicle suspension system and an active–passive tuned mass damper (TMD) system, are presented. The improvement of the overall system performance is also presented in comparison with conventional design methods.

Considering the Linear Parameter Varying (LPV) systems of discrete time, in this paper an approach for the synthesis of robust Proporcional+Integral Observers (PIO) is presented. From LPV systems characterized with polytopical uncertainties, the method of design is based on considering a dynamics extended of the typical PIO, in order to transform the design of the matrices of the dynamics of the observer, as a design of the gain of Static Output Feedback (SOF) of a problem of robust control. Under these conditions and from the norms H2=H1 described as Linear Matrix Inequalities (LMI), the criteria to obtain the gain in the SOF problem are established; taking into account performance indices in H2 and H1, under the presence of uncertainties and disturbances.