scholarly journals Modified Infinite-Time State-Dependent Riccati Equation Method for Nonlinear Affine Systems: Quadrotor Control

2021 ◽  
Vol 11 (22) ◽  
pp. 10714
Author(s):  
Sławomir Stępień ◽  
Paulina Superczyńska
Keyword(s):  
Riccati Equation ◽  
Control Process ◽  
Suboptimal Control ◽  
Algebraic Riccati Equation ◽  
Control Technique ◽  
Infinite Time ◽  
State Dependent ◽  
Independent Form ◽  
Penrose Pseudoinverse ◽  
Affine Nonlinear Systems

This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the problem. As a new contribution, the paper proposes a modified SDRE-based suboptimal control technique for affine nonlinear systems. The method uses a pseudolinearization of the closed-loop system employing Moore–Penrose pseudoinverse. Then, the algebraic Riccati equation (ARE), related to the feedback compensator gain, is reduced to state-independent form, and the solution can be computed only once in the whole control process. The ARE equation is applied to the problem reported in this study that provides general formulation and stability analysis. The effectiveness of the proposed control technique is demonstrated through the use of simulation results for a quadrotor device.

Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

2018 ◽  
Vol 41 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Yazdan Batmani
Keyword(s):  
Riccati Equation ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Design Procedure ◽  
The State ◽  
Suboptimal Control ◽  
Control Law ◽  
Closed Loop System ◽  
Infinite Time ◽  
State Dependent

In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.

scholarly journals Numerical Solution of SDRE Control Problem – Comparison of the Selected Methods

2020 ◽  
Vol 45 (2) ◽  
pp. 79-95
Author(s):  
Krzysztof Hałas ◽  
Eugeniusz Krysiak ◽  
Tomasz Hałas ◽  
Sławomir Stępień
Keyword(s):  
Control Systems ◽  
Riccati Equation ◽  
Computational Effort ◽  
Linear Control ◽  
Algebraic Riccati Equation ◽  
Linear Control Systems ◽  
Nonlinear Constraints ◽  
State Dependent ◽  
Suboptimal Solution ◽  
Problem Comparison

AbstractMethods for solving non-linear control systems are still being developed. For many industrial devices and systems, quick and accurate regulators are investigated and required. The most effective and promising for nonlinear systems control is a State-Dependent Riccati Equation method (SDRE). In SDRE, the problem consists of finding the suboptimal solution for a given objective function considering nonlinear constraints. For this purpose, SDRE methods need improvement.In this paper, various numerical methods for solving the SDRE problem, i.e. algebraic Riccati equation, are discussed and tested. The time of computation and computational effort is presented and compared considering selected nonlinear control plants.

Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

2022 ◽  
pp. 095441002110455
Author(s):  
Peichao Mi ◽  
Qingxian Wu ◽  
Yuhui Wang
Keyword(s):  
Riccati Equation ◽  
Linear Part ◽  
Suboptimal Control ◽  
Algebraic Riccati Equation ◽  
High Dimensional ◽  
Control Law ◽  
Chebyshev Series ◽  
Koopman Operator ◽  
Near Space ◽  
Error Dynamics

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Discrete Time-Coupled State-Dependent Riccati Equation Control of Nonlinear Mechatronic Systems

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Xin Wang
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Disturbance Attenuation ◽  
Infinite Time ◽  
Mechatronic Systems ◽  
Feedback Controllers ◽  
Control Laws ◽  
State Dependent ◽  
Time Optimal ◽  
Nonlinear Plant

Abstract A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and H∞ robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H∞ disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite and infinite time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.

scholarly journals Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Shaowei Zhou ◽  
Weihai Zhang
Keyword(s):  
Semidefinite Programming ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Stochastic Systems ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Infinite Time ◽  
Lq Problem ◽  
Lq Control

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.

A nonlinear robust optimal controller for an active transfemoral prosthesis: An estimator-based state-dependent Riccati equation approach

2020 ◽  
pp. 095965182095988
Author(s):  
Anna Bavarsad ◽  
Ahmad Fakharian ◽  
Mohammad Bagher Menhaj
Keyword(s):  
Energy Consumption ◽  
Riccati Equation ◽  
Sliding Mode ◽  
Parametric Uncertainty ◽  
Tracking Performance ◽  
Control Technique ◽  
Optimal Controller ◽  
State Variables ◽  
State Dependent ◽  
Nonlinear Robust

This article presents an estimator-based nonlinear robust optimal controller for an active prosthetic leg for transfemoral amputees. The proposed controller is derived from a combination of the state-dependent Riccati equation technique to optimize the energy consumption of the robot/prosthesis system and the sliding mode control to reduce the effects of the model parametric uncertainties and ground reaction forces as nonparametric uncertainties. In addition, the integral state control technique is employed to improve tracking; also, to have a compromise between tracking performance and control signal chattering, the boundary layer is then used. In this study, the performance of both the controller and estimator in the presence of noise and disturbance is assessed for nominal system while ±40% parametric uncertainty with respect to saturation bounds of control signals is considered. The results of the simulation in this research with ±40% parametric uncertainty compared to a robust adaptive impedance control approach with the only variation of ±30% on the system parameters, show high performance of the proposed controllers in reducing energy consumption, good robustness, improved position tracking performance, and good performance in estimating state variables, even in the presence of large initial errors compared to the extended Kalman filter.

scholarly journals Design of Satellite Attitude Control Algorithm Based on the SDRE Method Using Gas Jets and Reaction Wheels

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Luiz C. G. de Souza ◽  
Victor M. R. Arena
Keyword(s):  
Attitude Control ◽  
Control Algorithm ◽  
Controller Design ◽  
Algorithm Design ◽  
Large Angle ◽  
Space Mission ◽  
Control Technique ◽  
Gas Jets ◽  
State Dependent ◽  
Highly Nonlinear

An experimental attitude control algorithm design using prototypes can minimize space mission costs by reducing the number of errors transmitted to the next phase of the project. The Space Mechanics and Control Division (DMC) of INPE is constructing a 3D simulator to supply the conditions for implementing and testing satellite control hardware and software. Satellite large angle maneuver makes the plant highly nonlinear and if the parameters of the system are not well determined, the plant can also present some level of uncertainty. As a result, controller designed by a linear control technique can have its performance and robustness degraded. In this paper the standard LQR linear controller and the SDRE controller associated with an SDRE filter are applied to design a controller for a nonlinear plant. The plant is similar to the DMC 3D satellite simulator where the unstructured uncertainties of the system are represented by process and measurements noise. In the sequel the State-Dependent Riccati Equation (SDRE) method is used to design and test an attitude control algorithm based on gas jets and reaction wheel torques to perform large angle maneuver in three axes. The SDRE controller design takes into account the effects of the plant nonlinearities and system noise which represents uncertainty. The SDRE controller performance and robustness are tested during the transition phase from angular velocity reductions to normal mode of operation with stringent pointing accuracy using a switching control algorithm based on minimum system energy. This work serves to validate the numerical simulator model and to verify the functionality of the control algorithm designed by the SDRE method.

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