Optimal periodic output feedback control: a continuous-time approach and a case study

This work considers the design of optimal static output feedback controllers with priori structural constraints for linear systems. The structural constraints impose individual elements of the feedback matrix to satisfy certain equality or inequality constraints. The barrier method is used to address an auxiliary minimization problem to attain an approximate solution to the original nonconvex constrained optimization problem. The Lagrange multiplier method is applied to derive necessary conditions for the optimal solution. An easy-to-implement algorithm based on the gradient descent method is developed to solve the auxiliary minimization problem, and the convergence of the algorithm is proven. The effectiveness of the proposed methodology is validated using two numerical examples.

Considers the standard nonlinear H/sup /spl infin// output feedback control problem and proposes a family of controllers to solve the problem. These controllers are parametrized by a strictly dissipative free system. The parametrization given extends some previous results on the parametrization in the case of state feedback. In the linear case, the parametrization is shown to be exactly reduced to the well-known parametrization of H/sup /spl infin// (sub)optimal output feedback controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, a robust method for the simultaneous coordinated design of the interline power flow controller (IPFC) and power system stabilizer (PSS) based on output feedback controllers in a single-machine infinite-bus power system for the enhancement of power systems low-frequency oscillations damping is presented. The Honey Bee Algorithm, which has a strong ability to find the most optimistic results, is employed to search for optimal IPFC and PSS output feedback controller parameters. A singular value decomposition method is utilized to select the most effective damping control signal of the IPFC output feedback controller. To assess the effectiveness and robustness of the proposed method, simulation studies are carried out for three operating conditions. Analysis of the results shows that the combined design has an excellent capability for damping a power system’s low-frequency oscillations. Moreover, system performance analysis under different operating conditions and performance indices shows the effectiveness of the proposed method even when a severe fault is applied.

This paper deals with suboptimal linear quadratic (LQ) output feedback control of linear discrete systems. It is shown that degree of freedoms by instrumental variables employed in this paper lead to much flexibility in obtaining a suboptimal LQ controller. An improved convex optimization method involving linear matrix inequalities (LMIs) is suggested to solve the matrix inequalities characterizing a solution of the suboptimal LQ problem. Of the major interest of this paper is an extension to a class of nonconvex LQ problems of large size arising in decentralized feedback, simultaneous control, periodic feedback control, etc. Illustrative examples demonstrate the validity of the proposed convex approximate approach to optimal LQ output feedback control. Also, it is shown that suboptimal LQ solutions obtained by the proposed method can be used as an initial feasible point of existing iterative LMI algorithms to improve the feasibility of the iterative methods. Copyright © 2007 John Wiley &amp; Sons, Ltd.

This paper presents a new algorithm for the design of linear controllers with special structural constraints imposed on the control gain matrix. This so called SLC (structured linear control) problem can be formulated with linear matrix inequalities (LMI's) with a nonconvex equality constraint. This class of problems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. The first is that many design specifications are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixed-order output feedback controller. The second contribution is to propose a linearization algorithm to search for a solution to the nonconvex SLC problems. This has the effect of adding a certain potential function to the nonconvex constraints to make them convex. The convexified matrix inequalities will not bring significant conservatism because they will ultimately go to zero, guaranteeing the feasibility of the original nonconvex problem. Numerical examples demonstrate the performance of the proposed algorithms and provide a comparison with some of the existing methods.

This paper presents a cost-effective design based on sensor reduction for backing-up control of a vehicle with triple trailers. To realize a cost-effective design, we newly derive two linear-matrix-inequality (LMI) conditions for a discrete Takagi-Sugeno fuzzy system. One is an optimal dynamic output feedback design that guarantees desired control performance. The other is an avoidance of jackknife phenomenon for the use of the optimal dynamic output feedback controller. Our results demonstrate that the proposed LMI-based design effectively achieves the backing-up control of the vehicle with triple trailers while avoiding the jackknife phenomenon. More importantly, we demonstrate that the designed optimal control can achieve the backing-up control without, at least, two potentiometers that were employed to measure the relative angles (of a vehicle with triple trailers) in our previous experiments. Since the relative angles directly relate to the jackknife phenomenon, the successful control results without two potentiometers are very interesting and important from the cost-effective design point of view.

Robust output feedback-based neuro-fuzzy controller for seismically excited tall buildings with ATMD accounting for variations in the type of supporting soil

Different modeling and control strategies for distributed systems described by partial differential equations, where the involved signals depend not only on a temporal but also on one or more spatial variables, are investigated. When applying an array of actuator/sensor pairs, a spatial discretization is induced and - assuming spatial invariance - the system can be modeled as an interconnection of identical subsystems together with boundary conditions. While centralized control methods quickly turn impractical for such systems due to the high number of input and output channels, low-complexity synthesis techniques based on either a spatial shift operator or on interconnection graphs offer a solution for this problem at the cost of some conservatism. In order to compare the methods with respect to performance and complexity in terms of computation and implementation, the simple model of the temperature distribution in a thin rod with two different boundary conditions is used. Three types of distributed controllers are compared to an optimal centralized output feedback controller, obtained using standard H ∞ -loopshaping.

The equivalent representation in the delta domain of the digital optimal compensation problem is provided and computed in this article. This problem concerns finding digital optimal full and reduced-order output feedback controllers for linear time-varying and time-invariant systems with white stochastic parameters. It can subsequently be solved in the delta domain using the strengthened optimal projection equations that we recently formulated in this domain as well. If the sampling rate becomes high, stating and solving the problem in the delta domain becomes necessary because the conventional discrete-time problem formulation and solution become ill-conditioned. In this article, by means of several numerical examples and compensator implementations, we demonstrate this phenomenon. To compute and quantify the improved performance when the sampling rate becomes high, a new delta-domain algorithm is developed. This algorithm computes the performance of arbitrary digital compensators for linear systems with white stochastic parameters. The principle application concerns nonconservative robust digital perturbation feedback control of nonlinear systems with high sampling rates.

This paper proposes designing an optimal static output feedback controller for a structural-acoustics coupled system as efficient control architecture. Modelling of sound transmission through a plate-cavity-plate system is presented. In this coupled structural acoustic system, an approximate series solution is assumed for the displacements of the plates and the pressure inside the cavity. The solution of the coupled system is obtained using Galarkin’s method. The system to be modeled is consisting of a rectangular cavity with two flexible plates, one at the top of the cavity while the other at the bottom and four other fixed boundaries. Piezoelectric pair patches are considered to be bonded to the top plate, and eachpair is assumed to produce a pure moment actuation. The top plate is exposed to an external pressure excitation due to a planar wave generated by a sound source mounted above the cavity. Displacements at the mid points are calculated for the upper and lower plates. In the control scheme, the controller gains have been optimally tuned using genetic algorithms. The proposed architecture is compared to the linear quadratic Gaussian state feedback controller. The two controllers are compared for the time responses. The proposed controller shows a superior performance with simple implementation requirements.

In this study, a nonlinear electric power steering (EPS) system dynamic model based on road disturbance and torque sensor noise is investigated. In this paper, a new method of determining assist coefficient is proposed to obtain good driverpsilas feel, which is only relative to vehicle velocity. Evaluation indexes and an augmented system combined with the state space model of EPS are obtained. Hinfin control theory is introduced to minimize road disturbance and sensor noise, and linear matrix inequalities (LMIs) method is employed to design an optimal Hinfin dynamic output feedback controller. Simulation results show that the controller has good robustness and can reduce the influence of disturbance. So it can maintain good driverpsilas feel and the systempsilas stability.

This paper presents the general relative orbit dynamics equations and GPS orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition maintenance of spacecraft formation using GPS code pseudo-ranges are presented. The orbit control of the Earth-Orbiter 1 (EO-1)/Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3D initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

This paper mainly focuses on the optimal output feedback control problem for multiplicative noise systems involving packet dropouts, input delays and measurement delays over networked control systems (NCSs). Our contributions are two-fold. Firstly, the optimal estimator for multiplicative noise systems with packet dropouts and measurement delays is first derived. Secondly, by using the maximum principle, the sufficient and necessary condition for the optimal control problem is given based on the known estimator.

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally, numerical examples are given to verify the proposed results.