Optimal Steady-State Regulation Research Articles

Optimal Steady-State Regulation by State Feedback

Optimal Steady-State Regulation by State Feedback

Optimal Steady-State Regulator Design for a Class of Nonlinear Systems With Arbitrary Relative Degree.

In this article, we consider the regulator design problem for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with arbitrary relative degree. The objective is to regulate the output of the nonlinear system to an optimal steady state that solves a constrained optimization problem, without computing the optimal solution in advance. By embedding saddle-point dynamics, both state and output-feedback-based regulators are proposed and the resulting closed-loop systems are modeled in standard singularly perturbed forms. By invoking the singular perturbation analysis, exponential stability is established under some regularity condition. Compared with the existing methods, the proposed regulators can deal with a class of nonlinear systems with uncertainties and arbitrary relative degree. Furthermore, the current results can include some recent works on the distributed optimization problem as special cases. Finally, the effectiveness of the proposed methods is validated through numerical simulations.

Distributed Optimal Steady-State Regulation for High-Order Multiagent Systems With External Disturbances

In this paper, a distributed optimal steady-state regulation problem is formulated and investigated for heterogeneous linear multi-agent systems subject to external disturbances. We aim to steer this high-order multi-agent network to a prescribed steady-state determined as the optimal solution of a resource allocation problem in a distributed way. To solve this problem, we employ an embedded control design and convert the formulated problem to two simpler subproblems. Then, both state-feedback and output feedback controls are presented under mild assumptions to solve this problem with disturbance rejection. Moreover, we extend these results to the case with only real-time gradient information by high-gain control techniques. Finally, numerical simulations verify their effectiveness.

Distributed coordination for a class of non‐linear multi‐agent systems with regulation constraints

In this paper, a multi-agent coordination problem with steady-state regulation constraints is investigated for a class of nonlinear systems. Unlike existing leader-following coordination formulations, the reference signal is not given by a dynamic autonomous leader but determined as the optimal solution of a distributed optimization problem. Furthermore, we consider a global constraint having noisy data observations for the optimization problem, which implies that reference signal is not trivially available with existing optimization algorithms. To handle those challenges, we present a passivity-based analysis and design approach by using only local objective function, local data observation and exchanged information from their neighbors. The proposed distributed algorithms are shown to achieve the optimal steady-state regulation by rejecting the unknown observation disturbances for passive nonlinear agents, which are persuasive in various practical problems. Applications and simulation examples are then given to verify the effectiveness of our design.

Optimal control of laminated plate integrated with piezoelectric sensor and actuator considering TSDT and meshfree method

Abstract In this paper, the element free galerkin (EFG) method based on third-order shear deformation theory (TSDT) is used to investigate shape and vibration control of piezoelectric laminated plate bonded with piezoelectric actuator and sensor layers. The electric potential distributions through the thickness for each piezoelectric layer are assumed to vary linearly. In addition, a closed-loop velocity feedback control and optimal steady-state regulator with output feedback algorithm is used for the active control of the static deflection as well as the dynamic response of the plates with bonded distributed piezoelectric sensors and actuators. Furthermore, the effects of the size of support and nodal density on the numerical accuracy are also investigated. The results indicate that, the accuracy and reliability of presented work have an excellent agreement with those of other available numerical approaches such as finite element and FSDT meshfree method.

Optimal Control of Laminated Plate with Piezoelectric Sensor and Actuator Layers

A closed-form solution for the optimal control of vibrations of a simply supported symmetric thin laminated plate integrated with piezoelectric layers is obtained. The piezoelectric layers act as the distributed sensors and actuators. The method of designing the optimal steady-state regulator with output feedback is employed. Responses for various design parameters are illustrated. The results may be useful for the purpose of comparing the numerical models and experimental results.

Closed-form solution for optimal control of laminated plate

A closed-form solution for the optimal control of flexural vibration of simply supported symmetric laminated plate is obtained. The method of designing the optimal steady-state regulator is employed. Results for both full state feedback and output feedback are presented. Results may be useful for the purpose of comparing the numerical model and experimental results.

On a general optimal algorithm for multirate output feedback controllers for linear stochastic periodic systems

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>