Class Of Robust Controllers Research Articles

Constraint-tree-driven modeling and distributed robust control for multi-vehicle cooperation at unsignalized intersections

This paper proposes a multi-vehicle cooperation method based on the virtual platoon concept for unsignalized intersections. The method consists of two levels, i.e. constraint-tree-driven modeling (CTM) strategy for the supervision level and distributed robust control (DRC) method for the execution level. After projecting the approaching vehicles to a virtual lane, the CTM strategy determines the conflict-free passing sequence and driving mode and forms multiple local virtual platoons (LVP). A constraint tree is then constructed, in which constraints with a unified equality formation are utilized to describe the geometry topology of all vehicles, regardless of leader or member. Then, a class of robust control is proposed to render each vehicle to follow its prescribed constraint. The control is designed based on third-order nonlinear vehicle dynamics. The uniform boundedness, uniform ultimate boundedness performance of the entire system and string stability of LVP have been proven by leveraging the Lyapunov stability theory. The simulation results confirm that the proposed method functions well under time-varying traffic volume. Furthermore, the proposed method significantly improves the fuel economy, driving comfort and safety under low traffic volume compared with baseline methods.

Fuzzy dynamical system approach for a dual-parameter hybrid-order robust control design

Robust control for uncertain dynamical systems is considered. The uncertainty is assumed to be bounded, and the fuzzy set theory is adopted to describe the bound. A new dual-parameter hybrid-order robust control design is then proposed in two steps. First, a class of robust controls is designed, taking the advantage of the flexibility in choosing the order and a design parameter. The controls are deterministic and are not IF–THEN fuzzy rules-based. Deterministic performance, including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed. Second, a fuzzy-set theoretic based performance index consisting of average and steady state system performance and control cost is proposed. A constrained optimization problem is formulated with the intension of minimizing the performance index. The objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index. We show that the solution to the optimization problem always exists. As a result, the resulting control design achieves two concurrent goals: guaranteeing deterministic performance as well as minimizing the performance index. The theory is illustrated by an unmanned aerial vehicle (UAV) system control design.

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

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.

Stackelberg-Theoretic Approach for Performance Improvement in Fuzzy Systems.

This paper investigates the robust control for dynamical systems subject to uncertainty. The uncertainty is assumed to be (possibly fast) time varying and bounded. The bound is unknown but lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We propose an approach for the robust control design which is implemented in two steps. First, a class of robust controls is proposed based on tunable parameters. The proposed controls are deterministic and are not conventionally IF-THEN rules based. By the Lyapunov minimax approach, we prove that the proposed controls are able to guarantee deterministic system performance, namely, uniform boundedness and ultimate uniform boundedness. Second, optima seeking from the proposed controls is considered to improve fuzzy system performance. We formulate the optima-seeking problem as a two-player (one leader and one follower) Stackelberg game by developing two cost functions, each of which is in charge of one tunable parameter (i.e., the player). Each cost function consists of an average fuzzy system performance index and the associated player's control effort. We show that the solution of the optimal design problem (i.e., the optima of the tunable parameters), which is called the Stackelberg strategy, always exists and how to obtain the backwards-induction outcome is provided. Simulation results on the walking control of a biped robot model are presented for demonstration.

Robust trajectory tracking control for uncertain mechanical systems: servo constraint-following and adaptation mechanism

The paper proposes a novel trajectory tracking control for uncertain mechanical systems. We reformulate the trajectory tracking control as a constraint-following problem. A new set of servo constraints are constructed to fulfill the requirement of trajectory tracking. By the advantage of the second-order form of constraints, the constraint forces required in the constraint-following are derived in an explicit form. The uncertainty considered in the mechanical system is time-varying and bounded. But the bound is unknown. An adaptation mechanism with leakage and dead-zone is designed. Based on the adaptation, a new class of robust control is proposed. The performance of the resulting controlled system, including uniform boundedness and uniform ultimate boundedness, is guaranteed.

A Novel Robust Constraint Force Servo Control for Under‐actuated Manipulator Systems: Fuzzy and Optimal

AbstractWe consider the control design for under‐actuated manipulator systems. The task is to drive the system to be close to a prescribed constraint. The system contains uncertainty. It is bounded where the bounding information is prescribed by a fuzzy set (e.g., the bound is close to 1). The initial condition is also prescribed by a fuzzy set. A class of robust control is proposed, which guarantees a deterministic performance. On top of that, the choice of a control design parameter is cast into a fuzzy‐theoretic setting. A performance index, consisting of accumulated fuzzy‐based system performance and control cost, is proposed. The optimal control design parameters, which minimize the performance index, can be obtained by solving two algebraic quartic (fourth‐order) equations. As a result, the control design problem, which addresses both fuzzy and optimal characteristics, is completely solved.

A New Approach to Control Design for Constraint-following for Fuzzy Mechanical Systems

A new approach to the control design for the constraint-following of fuzzy mechanical system is proposed in this paper. We consider the mechanical system containing uncertainty, which may be nonlinear and fast time varying. The uncertainty is assumed to be bounded, and the bound of the uncertainty lies within a prescribed fuzzy set. A class of robust controls is proposed, and the corresponding adaptive law is constructed to emulate a constant parameter related to the bound of the uncertainty. The control scheme is deterministic and is not if-then rule based. Furthermore, we formulate the gain design of the adaptive law as a constrained optimization problem, which minimizes both the average fuzzy performance and the control effort. It is proved that the global solution to this optimization problem exists and is unique. The closed-form solution and the closed-form minimum cost are presented. The resulting adaptive robust control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the uncertain system regardless of the uncertainty, while minimizing the average fuzzy performance and control effort.

A New Approach to the Control Design of Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

On the Newton method in robust control of fluid flow

In this article we consider the Newton method for the numerical solution of a class ofrobust control problems in fluid mechanics recently studied in [5].We prove the local convergence of the algorithm and we obtain the rate of convergence of themethod.

ROBUST CONTROL DESIGN FOR A CLASS OF MISMATCHED COUPLED UNCERTAIN SYSTEMS

We consider a control design problem for a class of mismatched uncertain systems. The uncertainty is (possibly fast) time-varying. A new way of characterizing the structure of uncertainty is submitted. A class of robust controls, which is based on the possible bound of uncertainty, is proposed. The result shown here renders some previous development in this area as a special case. Illustrative examples include ecological systems, chemical reaction processes, electromechanical systems and heating processes. © 1997 John Wiley & Sons, Ltd.

A New Matching Condition for Nonlinear Robust Control Design

We study the control design problem for uncertain nonlinear systems. A new matching condition is presented. The main idea is to explore the route through which the (worst case) uncertainty may affect the stability. This route is then used to establish the new matching condition. Compared with the previous case, the current matching condition prescribes the route nonlinearly while the early matching condition is a special case of the linear description. A class of robust controls, which guarantees practical stability, can be designed based on this new matching condition. The size of the uniform ultimate boundedness ball can be made arbitrarily small by an appropriate choice of a design parameter.