Rigid spacecraft robust optimal attitude stabilization under actuator misalignments

In this paper, insulin injection process in which the level of glucose is monitored and corrected using optimal robust controller. The Bergman minimal model with unknown parameters was adopted to simulate a diabetes mellitus patient. An exogenous disturbance is considered as a meal effect on the patient. Optimal control approach to robust control design is suggested for glucose problem. The goal is to design a state feedback to stabilize the glucose system under uncertainty and disturbance. Linearized model of glucose system is considered with nonlinearity is lumped as a matched and mismatched uncertainties. Comparison in performance is made between the robust optimal controllers with classical optimal controller. The simulated results showed that the robust optimal controller outperforms the classical optimal controller for the considered cases. Also, the disturbance rejection capability of both controllers has been examined, and the results showed that the robust optimal controller has better rejection characteristics than its counterpart.

In this paper, the problem of the robust optimal control (ROC) for a class of nonlinear systems with uncertainties and external disturbances is studied. For this purpose, the State Dependent Riccati Equation (SDRE) is considered as a solution of the ROC. The proposed method is to transform a robust control problem into an optimal control problem, where the uncertainties and disturbances are reflected in the performance index. Hence, the performance index is selected as an energy function and using the proposed constraints in this paper the Lyapunov stability for this class of nonlinear systems is proved and the robust optimal controller is designed. In order to illustrate the high capability of the ROC method in optimal control of complex systems such as Hyper-chaotic system, the time response of state variables in the proposed method and the Global Robust Optimal Sliding Mode Control (GROSMC) method are compared together. The simulation results show that the time response of state variables in the ROC method is more sufficient than the GROSMC method.

The problem of synthesis of l/sub 1/ optimal robust controller for SISO plant under coprime factor perturbations and bounded external disturbance is considered. A geometric interpretation of l/sub 1/ optimal robust controller, standard l/sub 1/ optimal controller, and two other optimal robust controllers is presented. The existence of l/sub 1/ optimal robust linear controller is proved and an algorithm for approximate solution of the problem is proposed. The algorithm is reduced to approximate solution of finite family of standard l/sub 1/ optimization problems.

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, interconnected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances are taken into account throughout the learning process, wherein the system’s dynamics and the disturbances are assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in approximating the optimal control policy precisely due to imperfect data and computational errors. In this paper, a novel data-driven robust policy iteration method is proposed to simultaneously solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the use of reinforcement learning to improve the quality of designing adaptive optimal controllers for engineering applications. Adaptive dynamic programming methods, in particular policy iteration (PI), are widely used in solving optimal control problems. However, due to the iterative nature of PI, the approximated optimal control policy may be inaccurate and imprecise. Especially, when using imperfect system’s measurements instead of the modelling information. This can result in causing the learned control policy to deviate from the actual optimal policy. This becomes more challenging in the existence of dynamic uncertainties and unknown external disturbances which corrupt the measurements and result in imperfect data. This work investigates the conditions on the uncertainties such that the proposed novel data-driven PI algorithm is robust to system’s uncertainties, unknown external disturbances and imperfect measurements. The approximated robust optimal control policy performs robustly in the existences of imperfect data and uncertainties, and at the same time is close enough to the optimal control policy.

Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.

In this article, we propose an adaptive robust nonlinear optimal sliding mode control (SMC) using the optimal homotopy asymptotic method (RNOSC‐OHAM) for maximizing wind power capture. Because of the unstable nature of the wind and the presence of uncertainties and disturbances in the structure of the wind turbine, the optimal controller cannot provide robustness against uncertainties. Hence, we integrated this approach with a proportional–integral–derivative SMC (PID‐SMC) scheme to ensure the robustness of the system. The presented hybrid control input signal involves two components: a nonlinear optimal control law that provides the optimal performance of the nominal system and an adaptive PID‐SMC law. The adaptive PID‐SMC law employs a PID sliding surface along with adaptive mechanisms to create the robustness of the nonlinear wind turbine system. The nonlinear optimal control policy is designed by addressing the partial differential Hamilton–Jacobi–Bellman (HJB) equation. This equation is approximated using the OHAM. This combination strategy reduces the final time of the optimal control problems, provides desired responses and improves performance. Additionally, the RNOSC‐OHAM controller facilitates the safe performance of the wind turbine under uncertainties and maximizes the wind power captured. To evaluate the performance of RNOSC‐OHAM, the results of the presented algorithm are compared with some existing control schemes. The results indicate that the designed RNOSC‐OHAM controller is very rapid and needs few iterations and computational costs. Indeed, the present control scheme exhibits the best characteristics and has the fastest transient response. The RNOSC‐OHAM controller offers a proper balance between enhancing aerodynamic power capture and minimizing low‐speed shaft fluctuations using a small control input.

SummaryThis paper proposes an optimal control method of an unmanned aerial helicopter (UAH) with unknown disturbances. Solving the Hamilton‐Jacobi‐Bellman (HJB) equation is considered as the common approach to design an optimal controller under a meaningful cost function when facing the nonlinear optimal control problem. However, the HJB equation is hard to solve even for a simple problem. The inverse optimal control method that avoids the difficulties of solving the HJB equation has been adopted. In this inverse optimal control approach, a stabilizing optimal control law and a particular cost function that are obtained by a control Lyapunov function are required. An integrator backstepping method is used in designing the optimal control law of the UAH. Furthermore, a disturbance‐observer–based control (DOBC) approach has been adopted in the optimal control law for dealing with the unknown disturbances of the UAH system. Simulation results have been given to certify the stability of the nonlinear UAH system and the validity of this developed control method.

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

Design of an intelligent optimal neural network-based tracking controller for nonholonomic mobile robot systems

Optimal control of Markovian jump systems via a neural network-based ADP iterative algorithm

This paper investigates the robust optimal formation control for the position subsystem of quadrotor unmanned aerial vehicles (UAVs) subject to external disturbances and collision constraints. To prevent collision with both members of the formation and external obstacles, a collision avoidance potential function is constructed using relative position and velocity information. The basic bounded control input can ensure the stable flight and collision avoidance of a quadrotor UAV system. Based on the approximate dynamic programming (ADP) framework and two‐player zero‐sum differential game theory, the optimal controller is designed to further enhance the control performance of the system. The optimal value function is approximated by a single layer neural network, which avoids solving complex nonlinear Hamilton‐JacobiIsaac (HJI) equation. The stability of the closed loop system is proved. The effectiveness of the robust optimal formation controller based on learning is validated through MATLAB simulation in two distinct scenarios.

In this paper, a new robust controller is proposed to improve the motion control performance of an autonomous four‐wheel steering vehicle. The vehicle is subject to time‐varying uncertainties caused by parameter perturbation and unmodeled disturbance. First of all, the vehicle motion control problem is modeled as a constraint‐following problem with the goal to drive the vehicle system to follow the given constraints. For safety reasons, inequality constraints are imposed on the lateral displacement of the vehicle. Next, the diffeomorphism mapping method is used to deal with the inequality constraints in the vehicle motion control, and the constrained lateral displacement space is mapped to an unbounded space. On this basis, a new multi‐parameter robust constraint‐following control is designed. Based on Lyapunov stability theory, the approximate constraint tracking performance of the path tracking system is proved. In order to make a trade‐off between the system performance and control cost, a multi‐parameter optimization problem is established, and the optimal robust controller is obtained. Last, the main theoretical results are verified by the Carsim‐Simulink co‐simulations.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

Modified robust optimal adaptive control for flight environment simulation system with heat transfer uncertainty

In this paper, we present a new approach for constructing a global robust optimal control based on Dynamical Neural Networks of a class of uncertain nonlinear system. The proposed control scheme herein is a combination of continuous controller and discontinuous controller. The former is an inverse optimal controller (IOC) based on a control Lyapunov function to globally stabilize a nominal system and to also minimize the meaningful cost functional without solving the partial Hamilton Jacobi-Bellman (HJB) equation indirectly; on the other hands, the latter is a sliding mode controller to compel all trajectories of uncertain system reaching its sliding surface to zero, and also reject entire effects of uncertainties. Eventually, uncertain system performs as nominal system that an asymptotic convergence of the uncertain DNN is guaranteed under proposed control scheme, and all stability analyses of the closed-loop signals are proven using Lyapunov-based analysis. The effectiveness of the proposed control scheme is illustrated by numerical simulations.