Approximately Optimal Disturbance Attenuation for Nonlinear Time-Delay Large-Scale Systems

A new feedforward and feedback optimal control law for a class of nonlinear systems with persistent disturbances is presented in this paper. By using a successive approximation approach (SAA), the original nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of analytical linear feedforward and feedback terms and a nonlinear compensation term which is the limit of the solution sequence for the adjoint vector differential equations. By using the finite-step iteration of nonlinear compensation sequence, we can obtain a feedforward and feedback suboptimal control law. A disturbance observer is designed to get a physically realizable controller. Simulation examples show the effectiveness of the approach.

This paper considers the global optimal control for nonlinear interconnected large-scale systems with respect to linear quadratic functional. A successive approximation procedure is proposed to design the feedforward feedback nearly optimal control law. By introducing the Successive Approximation Approach of the nonlinear differential equation theory, a nonhomogeneous linear two-point boundary value problem sequence is constructed to approximate the nonlinear large-scale two-point boundary value problem, which is the necessary condition of the nonlinear control problem. By iteratively solving this nonhomogeneous linear approximating sequence, a global nearly optimal control law that composed of a linear closed-loop feedback compensatory term and an open-loop feedforward compensatory term is designed. An algorithm is presented to design certain qualified nearly optimal control law by truncating an infinite iteration result. An illustrative example shows the validity of the algorithm.

This paper studies disturbance rejection problem for discrete time-delay nonlinear systems. The optimal control of original systems causes a nonlinear Two Points Boundary Value (TPBV) problem with both time-delay terms and time-advanced terms. By using of Successive Approximation Approach (SAA), the original nonlinear TPBV problem is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay terms and time-advanced terms. We proved that the sequence of solutions uniformly converges to the optimal disturbance rejection control law of the original systems through two lemmas. By finite iterations of the solution sequence, the iterative procedure can be stopped and suboptimal control law is obtained. Based on reduced-order disturbance observer, the presented control law can be easily completed and physically realizable. Simulation results of two cases verify the validity and effectiveness of the presented controller.

This note focuses on the optimal output tracking control (OOTC) problem of a class of nonlinear systems with state time-delay. By using a successive approximation approach (SAA), the OOTC problem is transformed into a sequence of linear inhomogeneous two-point boundary value (TPBV) problems including adjoint vector differential equations. An iterative procedure is presented to solve the adjoint vector sequence. The OOTC law obtained consists of an accurate state feedback term, a feedforward term and a compensation term which is the limit of the adjoint vector sequence. Using a finite-time iteration of the adjoint vector among optimal solution sequence, we can obtain a suboptimal output tracking control (SOTC) law. A simulation example is employed to test the validity of the SAA

This paper develops an approximate design procedure of optimal tracking controllers for a class of nonlinear systems with persistent disturbances in the infinite time domain. By using the successive approximation approach (SAA), the two-point boundary value (TPBV) problem, which is derived from the optimal control theory, is transformed into solving a sequence of linear TPBV problems. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original optimal tracking control (OTC) problem. A feedforward and feedback optimal tracking control (FFOTC) law is derived from a Riccati equation, matrix equations and a sequence of adjoint vectors. The existence and uniqueness conditions of the FFOTC are given. At last, a design algorithm of solving the approximate FFOTC law is proposed, and simulation results demonstrate the validity of the algorithm.

This paper presents the approximate optimal vibration control methodology for discrete nonlinear vehicle active suspension subject to persistent road disturbances. Based on a dynamic model of nonlinear vehicle active suspension and a linear exogenous system model of the persistent road disturbances, a nonlinear two-point boundary value (TPBV) problem is introduced. By introducing a sensitive parameter, the original TPBV problem is reformed as a series of TPBV problems without nonlinear items. A discrete approximate optimal vibration controller (DAOVC) can be obtained by solving a Riccati equation, Stein equation, and nonlinear compensation item, respectively. An iteration algorithm is designed to realize the computational realizability of DAOVC based on the control performance. It is demonstrated that the control performance of ride comfort, road holding ability, and suspension deflection under the DAOVC are much smaller than the ones under the classical feedforward and feedback optimal vibration controller (FFOVC) and open-loop vehicle suspension system.

Decentralized optimal controller design for multimachine power systems using successive approximation approach

The optimal output tracking control problem for nonlinear large-scale dynamic systems is considered. A series-based approximate approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value problem is transformed into a sequence of linear decoupling two-point boundary value problems. By intercepting the frontal finite terms of the solution series, we obtained a suboptimal tracking control law. A simulation example illustrates the efficiency of the optimal output tracking control law designed.

An efficient parallel processing optimal control scheme for a class of nonlinear composite systems

The problem of designing nonlinear sliding manifolds with a quadratic performance index for a class of nonlinear systems is considered. By applying optimal quadratic control theory to constructing sliding manifolds, nonlinear two-point boundary value (TPBV) problems are induced. Then a novel sensitivity approach is introduced to transform the original problems into solving a series of nonhomogeneous linear TPBV recursive formulas. By finite terms recursion, we obtain approximate solutions of optimal sliding manifolds. The procedure to get the suboptimal sliding manifolds is presented in detail. Employing the reaching law approach, we select a control input that can force the system states to reach the nonlinear sliding manifold in finite time and have low chattering in the sliding motion. An example is given for illustration.

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

A decentralized adaptive control method is proposed for large-scale systems with unknown time-delayed nonlinear interconnections unmatched in control inputs. It is assumed that the time-delayed interaction terms are bounded by unknown nonlinear bounding functions. The nonlinear bounding functions and uncertain nonlinear functions of large-scale systems are compensated by the function approximation technique using neural networks. The dynamic surface control method is extended to design the proposed memoryless local controller for each subsystem of uncertain nonlinear large-scale time delay systems. Therefore, although the interconnected systems consist of a large number of subsystems, the proposed controller can be designed simply. We prove that all the signals in the total closed-loop system are semiglobally uniformly bounded and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is given to demonstrate the effectiveness and applicability of the proposed scheme.

In order to improve the stability and performance of an autonomous vehicle, optimization needs to be explicitly performed in the controllers, which has an essential part in the tracking system. This work proposes a novel longitudinal control optimization scheme and a novel longitudinal controller consisting of a feed-forward and feedback term. The feed-forward term is inspired by the vehicle’s steady-state response, whereas the feedback term is a proportional-integral-derivative (PID) controller. Also, a model representing the longitudinal vehicle dynamics is designed based on physical phenomena affecting the vehicle. Besides, some nature-inspired optimization algorithms are used to determine the optimal model parameters and optimize the controller parameters, i.e., Particle Swarm Optimization (PSO), Accelerated PSO (APSO), Flower Pollination Algorithm (FPA), and Modified FPA (MFPA). The algorithms are compared in optimizing the longitudinal vehicle model and controller using the CARLA simulator, and stability tests are also done for each algorithm. In addition, the characteristics of several cost functions in controller optimization are inspected. The results show that the MFPA is the most stable algorithm, the proposed model represents the system satisfactorily, and optimizing the controller using a regularized cost function leads to better overall performance. Our code is available in https://github.com/fadamsyah/Particle-Based-Optimization-for-Longitudinal-Control.

The problem of tracking a reference variable from a given class is considered for discrete-time linear single-input-output plants. The plant and the reference are both described by an input/output relation, such as a difference equation, and the objective is to track exactly in a minimum time. This dead-beat servo problem is solved hero by applying polynomial techniques. The optimal control law is shown to contain both feed-back and feed-forward terms and it is obtained by solving two linear polynomial equations. The entire design procedure is remarkably simple and efficient.

The problem of optimal vibration control for nonlinear vehicle suspensions based on in-vehicle networks is considered. The paper addresses this problem to design a suboptimal vibration controller for nonlinear sampled-data system with actuator and sensor delays. Employing the successive approximation approach, the nonlinear suboptimal control law is derived from a Riccati equation, a Stein equation, and sequences of adjoint vector difference equations, which consists of a feedback and feedforward term, a nonlinear compensator term, and some control memory terms. The existence and uniqueness of the optimal control law are proved. Furthermore, the controller is applied into a quarter-car suspension model and numerical simulations are given. Based on the analysis and simulations, the results validate the effectiveness of the designed control. And the proposed approach is feasible and easy to implement.