Sub-Optimal Control for Nonlinear Heat Equations

2012 ◽  
Vol 217-219 ◽  
pp. 2488-2491
Author(s):  
Xi Ju Zong ◽  
Xin Gong Cheng ◽  
Yong Zhang
Keyword(s):  
Optimal Control ◽  
Suboptimal Control ◽  
Linear Feedback ◽  
Control Law ◽  
Heat Equations ◽  
Nonlinear Heat Equations ◽  
Nonlinear Compensation ◽  
Linear Differential ◽  
Finite Step ◽  
Successive Approximation Approach

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear heat equations with a quadratic performance index. By using the SAA, the optimal control problem for nonlinear heat equations is transformed into a sequence of nonhomogeneous linear differential Riccati operator equations. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoin vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law.

A Successive Approximation Approach of Nonlinear Optimal Control with R-Rank Persistent Disturbances

2011 ◽  
Vol 130-134 ◽  
pp. 1862-1866
Author(s):  
Shi Yong Ma
Keyword(s):  
Optimal Control ◽  
Successive Approximation ◽  
Nonlinear Optimal Control ◽  
Suboptimal Control ◽  
Control Law ◽  
Approximation Approach ◽  
Nonlinear Compensation ◽  
Successive Approximation Approach ◽  
Feedback Optimal Control ◽  
Persistent Disturbances

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.

scholarly journals Congestion Control for Nonlinear TD-SCDMA Discrete Networks Based on TCP/IP

2015 ◽  
Vol 11 (7) ◽  
pp. 21
Author(s):  
Peng Liu
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Successive Approximation ◽  
Network Control ◽  
Control Law ◽  
Approximation Approach ◽  
Solution Sequence ◽  
Network Control Systems ◽  
Nonlinear Compensation ◽  
Successive Approximation Approach

A successive approximation approach (SAA) is developed to obtain a new congestion controller for the nonlinear TD-SCDMA network control systems based on TCP/IP. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term that is the limit of the solution sequence of the adjoint vector differential equations. By using the finite-time iteration of nonlinear compensation term of optimal solution sequence, we can obtain a suboptimal control law for TD-SCDMA network control systems based on TCP/IP.

Decentralized observer-based optimal control using two-point boundary value successive approximation approach application for a multimachine power system

2020 ◽  
Vol 42 (9) ◽  
pp. 1641-1653 ◽  
Author(s):  
Basma Abidi ◽  
Salwa Elloumi
Keyword(s):  
Optimal Control ◽  
Power System ◽  
Successive Approximation ◽  
Boundary Value ◽  
Suboptimal Control ◽  
Control Law ◽  
Point Boundary ◽  
Approximation Approach ◽  
Successive Approximation Approach ◽  
Decentralized Observer

In this paper, we present a new decentralized observer for a class of nonlinear interconnected systems, based on an optimal control law using the two-point boundary value (TPBV) successive approximation approach. This technique, used previously to develop a nonlinear decentralized suboptimal control for a multimachine power system, inspired us to develop a new method to design a decentralized observer-based suboptimal control law for the same system. The TPBV approach is characterized by the transformation of each high order coupling nonlinear TPBV problem into a sequence of linear decoupling TPBV problems that uniformly converge to the optimal control for nonlinear interconnected large-scale systems. Sufficient conditions for the asymptotic stability of the developed feedback control scheme are proposed in terms of linear matrix inequalities (LMIs) constraints, which can be efficiently solved by the LMI optimization techniques, to compute the control and the observation gains of the overall system. We applied this approach to a three-machine power system which generators are nonlinear systems strongly interconnected. We demonstrated clearly, via advanced simulations, that this approach was able to bring good performances, improving effectively transient stability of this power system in few iterative sequences while allowing the reconstruction of its non-measurable state variables.

scholarly journals Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

2022 ◽  
Author(s):  
Peichao Mi ◽  
Qingxian Wu ◽  
Yuhui Wang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Attitude Control ◽  
Stable Manifold ◽  
Closed Loop ◽  
Suboptimal Control ◽  
Control Law ◽  
Attitude Dynamics ◽  
Attitude Control System ◽  
Near Space

Abstract This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

Trajectory Control of Miniature Helicopters Using a Unified Nonlinear Optimal Control Technique

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ming Xin ◽  
Yunjun Xu ◽  
Ricky Hopkins
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
Suboptimal Control ◽  
Control Technique ◽  
Control Law ◽  
Wind Gust ◽  
Flight Envelope ◽  
Time Optimal

It is always a challenge to design a real-time optimal full flight envelope controller for a miniature helicopter due to the nonlinear, underactuated, uncertain, and highly coupled nature of its dynamics. This paper integrates the control of translational, rotational, and flapping motions of a simulated miniature aerobatic helicopter in one unified optimal control framework. In particular, a recently developed real-time nonlinear optimal control method, called the θ-D technique, is employed to solve the resultant challenging problem considering the full nonlinear dynamics without gain scheduling techniques and timescale separations. The uniqueness of the θ-D method is its ability to obtain an approximate analytical solution to the Hamilton–Jacobi–Bellman equation, which leads to a closed-form suboptimal control law. As a result, it can provide a great advantage in real-time implementation without a high computational load. Two complex trajectory tracking scenarios are used to evaluate the control capabilities of the proposed method in full flight envelope. Realistic uncertainties in modeling parameters and the wind gust condition are included in the simulation for the purpose of demonstrating the robustness of the proposed control law.

scholarly journals Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

2021 ◽  
Author(s):  
Peichao Mi ◽  
Qingxian Wu ◽  
Yuhui Wang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Attitude Control ◽  
Stable Manifold ◽  
Closed Loop ◽  
Suboptimal Control ◽  
Control Law ◽  
Attitude Dynamics ◽  
Attitude Control System ◽  
Near Space

Abstract This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

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