Stabilizing receding horizon H/sub ∞/ controls for linear continuous time-varying systems

A general receding horizon predictive control (RHPC), or model predictive control (MPC), for time-delay systems is proposed. The proposed RHPC is obtained by minimizing a new cost that includes two terminal weighting terms, which are closely related to the closed-loop stability. The general solution of the proposed RHPC is derived using the generalized Riccati method. Furthermore, an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size. A linear matrix inequality (LMI) condition on the terminal weighting matrices is proposed, under which the optimal cost is guaranteed to be monotonically non-increasing. It is shown that the monotonic condition of the optimal cost guarantees closed-loop stability of the RHPC. Simulations demonstrate that the proposed RHPC effectively stabilizes time-delay systems.

Global stabilization for linear continuous time-varying systems

A linear continuous time-varying system and a sample-data system with continuous time-varying linear part are considered. For both systems a two-dimensional control is formed which provides an invariant stabilization of a closed loop system. I. INTRODUCTION The invariant stabilization problem deals with such stabi- lization which provides an independence of output from outer action and boundedness of other variables. As demonstrated in (1-3) this problem remains one of the most actual in the theory of control systems. The main conclusion of these papers is: beginning from linear stationary systems the scalar control can provide either stability or invariance. A statement in (4) says that for a linear stationary system it is possible to combine the requirements of invariance and stability if the outer action is considered as one of the regulator's input. In the present report a linear continuous time-varying system and a sample-data system with continuous time- varying linear part are considered. For both systems a two- dimensional control is formed which provides an invariant stabilization of a closed loop system. If the vector of ob- servation is orthogonal to the vector of outer action the measurement of the action is not required. II. LINEAR NONSTATIONARY SYSTEM The following system

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.

This paper focuses on the synthesis problem of robust and reliable H/sup /spl infin// control for linear systems with norm-bounded time-varying parameter uncertainty in the state and delayed-state matrices, and also with actuator failures among a pre-specified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. A linear matrix inequality (LMI) method is given for the memoryless state feedback synthesis problem to quadratically stabilize the given systems with H/sup /spl infin//-norm bound constraints on attenuation of augmented disturbances, including failure signals in cases of actuator failures for any admissible uncertainty. The results depend on the size of the time-delay via the use of a Razumikhin-type theorem.

Microgrids are gaining considerable attention due to the installation of renewable power generation resources in areas that are closer to the load centers. The multivariable droop idea, acknowledges active power sharing by concurrent drooping of both voltage and frequency, in resistance as well as weak grids. To develop a multivariable-droop synchronous current converter control strategy for current management using Lyapunov stability of microgrid applications. In this paper overview of Lyapunov stability of linear continuous systems is presented. The conditions for the existence of the solutions for both regular and irregular singular linear systems are introduced. To guarantee an asymptotical stability for linear continuous singular systems and new stability conditions are analyzed. A considerable attention is focused on the design of controllers for multivariable linear systems so that certain system properties could be preserved under various classes of perturbations occurring in the system. It presents a multivariable-droop synchronous current converter control strategy for current management of weak grid/microgrid applications, and offers a systematic and straightforward design approach using the loop shaping technique. The controller integrates current regulation, management, and limitation that are applicable to microgrids (MGs). The simulation is done by MATLAB/SIMULINK software.

CRONE control of continuous linear time periodic systems: Application to a testing bench

The notions of poles and zeros at infinity and their relations are extended to the case of linear continuous time-varying systems. This study is based on the notion of a newborn systems which is, in a mathematical point of view, a graded module extension over the noncommutative ring of differential operators. It is proved to be a relevant generalization to the time-varying case of the class, for the so-called restricted equivalence of Rosenbrock's polynomial matrix descriptions. The authors' approach is intrinsic and unifies the definitions previously given in the literature in the time-invariant case.

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

Discretization of continuous linear dynamic systems. Analysis of the methods

The paper is concerned with the problem of non-fragile H/sub /spl infin// controller design for linear time-invariant systems. The controller to be designed is assumed to have multiplicative gain variations. Design methods are presented in terms of symmetric positive-definite solutions of algebraic Riccati inequalities. The resulting design is such that the closed-loop system is robustly stable and has an H/sub /spl infin// disturbance attenuation bound with respect to the multiplicative controller gain variations. A numerical example is given to illustrate the design methods.

The optimal output tracking control(OOTC) problem is considered for continuous linear time-invariable systems, which include control delays and external sinusoidal disturbances. We first transform the original system into a new system without time-delay, then construct a new state vector, which containing a external system’s vector. The external system described the aim which we want to track. Following the law of internal model principle, we transform the original and external systems into a new augmented system. Finally we get an optimal control law according to the optimal performance index, and prove the method is effective by emulation.