Showing papers by "Ye-Hwa Chen published in 2019"

Vehicle motion control under equality and inequality constraints: a diffeomorphism approach

Abstract: This study addresses the problem of vehicle lateral and yaw motion control when both equality and inequality (i.e., bilateral and unilateral) constraints are involved. By using the Udwadia–Kalaba approach, the explicit equation of vehicle motion with equality constraints is established, and the corresponding control inputs can be obtained from the equation. The equality constraints aim to render the vehicle to move along the desired trajectory. However, as the initial conditions of vehicle motion may take values leading the vehicle to violate the road-bound lines, it is necessary to impose an additional constraint to constrain the vehicle to move within the road-bound lines, which is an inequality constraint. As the inequality constraint cannot be handled by the original Udwadia–Kalaba approach, a creative diffeomorphism approach is proposed to integrate the inequality constraint into the equality constraints, and thus it creatively enables the Udwadia–Kalaba approach to deal with both equality and inequality constraints. By solving the equation established based on the Udwadia–Kalaba approach and diffeomorphism approach, the control inputs that can render the vehicle to move along the desired trajectory without violating the road-bound lines are obtained. The effectiveness of the proposed method is demonstrated by numerical simulation results.

Nash-Game-Oriented Optimal Design in Controlling Fuzzy Dynamical Systems

Abstract: The robust control design problem for uncertain dynamical systems is considered in this study. The uncertainty is time varying (possibly fast) and bounded, and the bound lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We design the robust control in two steps. First, we propose a class of robust controls based on tunable parameters, which is in deterministic form and not conventionally IF–THEN fuzzy rule based. It is shown that these controls are able to guarantee deterministic system performance, namely uniform boundedness and ultimate uniform boundedness. Second, we seek the optima of tunable parameters in the control by formulating a two-player Nash game, which is based on two performance indexes (i.e., the cost functions). It is shown that the Nash equilibrium (i.e., the optima of tunable parameters) always exists. The procedure of obtaining the Nash equilibrium is provided. Under the proposed control, the system performance is both deterministically guaranteed and fuzzily optimized from the Nash game perspective. The effectiveness of the control design is illustrated by the simulation control of a unicycle robot.

Optimal Design of Robust Control for Fuzzy Mechanical Systems: Performance-Based Leakage and Confidence-Index Measure

Abstract: The optimal design problem of adaptive robust control for fuzzy mechanical systems with uncertainty is investigated in this paper. The uncertainty that may be nonlinear and (possibly fast) time-varying is assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. Based on the Udwadia and Kalaba's approach, an adaptive robust controller, which is deterministic and is not the usual if-then rules-based is proposed to render the system to follow a class of prespecified constraints approximately. The adaptive law is of leakage type that can adjust the magnitude of the adaptive parameter based on the nonlinear performance-dependent gain. The resulting controlled system is uniformly bounded and uniformly ultimately bounded, which is proved via the Lyapunov minimax approach. Furthermore, we propose a novel concept: fuzzy confidence to measure the expectation value of a fuzzy number. Then, a fuzzy-based system performance index that includes the expectation value of the uniform ultimate boundedness (the average fuzzy performance) and the control cost is formulated. The optimal design problem associated with the control can then be solved by minimizing the performance index. As a result, the performance of the fuzzy mechanical system is both deterministically guaranteed and fuzzily optimized under this control.

Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

Abstract: Controlling underactuated systems is a challenging problem in control engineering. This paper presents a novel constraint-following approach for control design of an underactuated two-wheeled mobile robot (2 WMR), which has two degrees-of-freedom (DOF) to be controlled but only one actuator. The control goal is to drive the 2 WMR to follow a set of constraints, which may be holonomic or nonholonomic constraints. The constraint is considered in a more general form than the previous studies on constraint-following control (hence including a wider range of constraints). No auxiliary variables or pseudo variables are required for the control design. The proposed control only uses physical variables. We show that the proposed control is able to deal with both holonomic and nonholonomic constraints by forcing the constraint-following error to converge to zero, even if the system is not initially on the constraint manifold. Using this control design, we investigate two cases regarding different constraints on the 2 WMR motion, one for a holonomic constraint and the other for a nonholonomic constraint. Simulation results show that the proposed control is able to drive the 2 WMR to follow the constraints in both cases. Furthermore, the standard linear quadratic regulator (LQR) control is applied as a comparison in the simulations, which reflects the advantage of the proposed control.

Rendering Optimal Design in Controlling Fuzzy Dynamical Systems: A Cooperative Game Approach

Abstract: This study investigates the robust control for uncertain dynamical systems. The uncertainty is (possibly fast) time-varying but bounded. We adopt the fuzzy set theory to describe the uncertainty in the system (hence, called the fuzzy dynamical system). A class of robust controls is proposed based on tunable parameters. The controls are deterministic and are not conventional IF–THEN fuzzy rules based (such as Mamdani type). The proposed controls are able to guarantee deterministic system performance, namely uniform boundedness and uniform ultimate boundedness. In the phase of searching for the optima from the pool of admissible control design parameters, we formulate this as a two-player cooperative game by developing two performance indexes (i.e., the cost functions), each of which is dominated by one tunable parameter (i.e., the player). By the cooperative game theory, we are able to obtain the Pareto-optimality (i.e., the optima of tunable parameters). Simulation results on an electric vehicle motion control problem are presented for demonstration.

Optimal Robust Position Control With Input Shaping for Flexible Solar Array Drive System: A Fuzzy-Set Theoretic Approach

Abstract: The position control and vibration suppression problems of the flexible solar array drive system containing uncertainty are considered in this paper. The uncertainty in system may be due to unknown parameters and external disturbance. The uncertainty bound can be described via a fuzzy set. In addition, there exists the flexible vibration in the system. A new optimal robust control approach with input shaping is proposed for the flexible solar array drive system. By designing the position command trajectory, the input shaper is proposed to suppress the flexible vibration. To enhance the position control performance, the optimal robust control is proposed by fuzzy description of the uncertainty bound. Neither the system nor the control is fuzzy if–then rule based. The global solution to this optimal design problem is demonstrated to be always existent and unique. The resulting control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while minimizing a fuzzy-based performance index associated with both the fuzzy performance and the control cost. In addition, the flexible vibration can be effectively suppressed. The novelty of this research is a systematic control approach by blending input shaping technology, control theory, fuzzy set theory, and optimization theory into an integrated framework, for solving the position control and vibration suppression problems of flexible solar array drive system with mismatched conditions.

Uniform ultimate boundedness for underactuated mechanical systems as mismatched uncertainty disappeared

Abstract: We propose to design control for uncertain underactuated mechanical systems. The underactuated mechanical system is to follow prescribed holonomic or nonholonomic constraints. The uncertainty in the system does not in general fall within the range space of the input matrix, which is a major obstacle for control design. To resolve this difficulty, we decompose the uncertainty into matched uncertainty and mismatched uncertainty in a unique manner using the geometric structural characteristics of the system. A control scheme is designed to guarantee uniform boundedness and uniform ultimate boundedness of a constraint-following performance measure. The control is based solely on the matched uncertainty. The mismatched uncertainty turns out to be disappeared, as far as the performance analysis is concerned, since it is orthogonal to the geometric space of interest. For demonstrations, a vehicle/inverted pendulum platform is selected. We charge the system to follow either holonomic or nonholonomic constraint. The simulation shows the system performance, in following the prescribed constraint, is superior.

Fuzzy-Set Theory Based Optimal Robust Design for Position Tracking Control of Permanent Magnet Linear Motor

Abstract: In this paper, we design an optimal robust control to address the problem of position tracking control for permanent magnet linear motor (PMLM). The uncertainties in PMLM system, including parameters uncertainty and external disturbance, are nonlinear and time-varying. The uncertainties are assumed to be bounded, and the bounds are described via fuzzy sets. Then, a model-based robust control in deterministic form is proposed. Furthermore, an optimal robust control for PMLM system is formulated as a fuzzy performance index optimization problem, which associated with both the fuzzy system performance and the control cost. The resulting optimal control can guarantee the uniform boundedness and uniform ultimate boundedness. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness of the optimal robust control for PMLM.

Controlling Uncertain Swarm Mechanical Systems: A $\beta$ -Measure-Based Approach

Abstract: We consider an artificial swarm mechanical system consisting of multiple agents. The agents are composed of mechanical components. The ideal kinematic performance includes mutual attractions and repulsions. This kinematic performance is embedded into the dynamics by being treated as a constraint. The Udwadia–Kalaba theory is then used to generate the required servo constraint force to assure the constraint is met for the nominal system. The system also includes uncertainty. The uncertainty in the swarm mechanical system is time-varying, whose value falls within a prescribed fuzzy set. For the robust control design, a creative $\beta$ -measure-based approach is introduced. The robust control guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of the uncertainty. For the optimal choice of a control design parameter, a fuzzy-theoretic performance index is introduced. The resulting optimization problem is proven to be tractable, with the global solution to be existent and unique. Furthermore, the analytic expression of this solution is obtained. As a result, the optimal design problem is completely solved. To further demonstrate its effectiveness, we compare the performances of the swarm mechanical system under the robust control and linear–quadratic regulator control through simulation results with an illustrative example.

Controlling the differential mobile robot with system uncertainty: Constraint-following and the adaptive robust method:

Abstract: We aim to control the differential mobile robot system to follow a class of pre-specified constraints sufficiently closely in the presence of system uncertainties. The mass and the moment of inerti...

Robust Observer Design and Fuzzy Optimization for Uncertain Dynamic Systems

Abstract: To achieve the state estimation of uncertain nonlinear systems, this paper proposes a novel optimal robust observer via the fuzzy bound information of the uncertainty. A robust observer scheme is first proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the state estimation system regardless of the actual value of the uncertainty. To optimize the observer gain, a fuzzy set-theoretic-based optimal approach is then proposed by utilizing the fuzzy information of the uncertainty bound. The optimization problem is completely solved in analytic form. The resulting observer is able to guarantee the robustness of the state estimation system to the uncertainty, while minimizing an optimization index related to the state estimation performance and the observer cost. The novelty of this research is a creative optimal robust observer design by blending state estimation theory, fuzzy set theory, and optimization theory into an integrated framework.

Optimal Design of Adaptive Robust Control for Fuzzy Swarm Robot Systems

Abstract: Motion control for an uncertain swarm robot system consisting of N robots is considered. The robots interact with each other through attractions and repulsions, which mimic some biological swarm systems. The uncertainty in the system is possibly fast time varying and bounded with unknown bound, which is assumed to be within a prescribed fuzzy set. On this premise, an adaptive robust control is proposed. Based on the proposed control, an optimal design problem under the fuzzy description of the uncertainty is formulated. This optimal problem is proven to be tractable, and the solution is unique. The solution to this optimal problem is expressed in the closed form. The performance of the resulting control is twofold. First, it assures the swarm robot system deterministic performances (uniform boundedness and uniform ultimate boundedness) regardless of the actual value of the uncertainty. Second, the minimization of a fuzzy-based performance index is assured. Therefore, the optimal design problem of the adaptive robust control for fuzzy swarm robot systems is completely solved.

A Hierarchical Robust Control Design With Non-Parallel Distributed Compensator and Application to Aircraft Engines

Abstract: This paper proposes a hierarchical multivariable robust control design for a class of uncertain nonlinear dynamic system. The dynamic system is described by an uncertain T-S fuzzy model. The uncertainties in the model are structure matched and norm-bounded. For this fuzzy model, a hierarchical robust control consisting of two level compensators is presented. While the level 1 compensator ensures the basic robust performance, the level 2 compensator restrains the uncertainty. Under this design, the controlled system is uniformly bounded and uniformly ultimately bounded. To illustrate the design approach, the application to a multivariable control of turbofan engines is discussed. The semi-physical simulations of the controlled turbofan show that the resulting control is able to guarantee the prescribed boundedness in a more practical condition.

Adaptive-Adaptive Robust (A 2 R) Control for Uncertain Mechanical Systems: Rendering $\beta$ -Ultimate Boundedness

Abstract: A novel control scheme, namely adaptive-adaptive robust (A 2 R) control is proposed for motion control of mechanical systems. The system contains uncertainty which is bounded while the bound may be unknown. Two designs of robust controls are proposed, with the first class featuring leakage type and the second class featuring dead-zone type. Each class involves an adaptive law with the intension of mimicking the uncertainty bound. However, there exists an undetermined design parameter in the adaptive law. An upper-layer adaptive law for the determination of this design parameter is then proposed; hence rendering the adaptive-adaptive robust (A 2 R) control. The control guarantees uniform boundedness and uniform ultimate boundedness of a resulting augmented system state, including a β-measure which reflects how close the constraint is followed.

Constraint-Following Control for Mobile Robots: A Hierarchical Approach

Abstract: This study addresses the problem of constraint-following control of mobile robots with different categories of constraints by using a hierarchical approach. The approach is proposed based on Udwadia-Kalaba theory. When unconstrained mobile robots with complex generalized coordinates applied structural constraints as well as motion constraints, the number of constraints may be large and difficult to handle. What is more, it is difficult to obtain the dynamic equation as well as the constraint-following control force of the constrained system. To solve these problems, the hierarchical approach is creatively proposed. Numerical simulations of the mobile robot are performed to demonstrate the efficacy and accuracy of this methodology.

Modern explorations of the Brachistochrone-related problem: using the Udwadia–Kalaba approach:

Abstract: Modern explorations regarding the search for a curve subject to a minimization principle and its inverse, namely the search for the minimization object based on a given curve, are made. By using th...

Adaptive Robust Constraint Following Control for Mechanical Systems

Abstract: The constraint following control problem of the mechanical systems is investigated in this paper. For the practical mechanical system, there always exists the time-varying uncertainty, which may be due to the system parameter perturbation, the modeling error, and the external disturbance. The uncertainty will result in the constraint following performance degradation. To solve this issue, a new adaptive robust control is proposed to force the system to satisfy the constraint. The control scheme consists of two parts: the nominal part and the adaptive robust part. The nominal part is proposed based on the Udwadia-Kalaba theory, which can guarantee the constraint following performance of the nominal system. The adaptive robust part is proposed to compensate for the uncertainty. In addition, the adaptive law is proposed to estimate the uncertainty bound of the system. The resulting adaptive robust control can guarantee the uniform boundedness and uniform ultimate boundedness of the constraint following system in the presence of various uncertainties, which is verified by a two-link Revolute-Prismatic Mechanical Manipulator (RPMM) system.