Robust controller design and experimental validation based on bounded uncertainty for collaborative industrial robots.

In this paper, derived from the proportional-derivative control and robust control, a novel practical robust control method based on a dynamic feedforward model is established by taking six-axis motion cooperative industrial robots as the research object. The nonlinear friction, parameter uncertainty, and external disturbance are taken into consideration while establishing the dynamic model of the cooperative industrial robot. The method includes a proportional-derivative control and a robust control. Lyapunov theory is used to analyze the proposed controller, and it is shown that this method can guarantee uniformly bounded and uniformly final bounded systems. Simulation and experiment results show that the proposed controller is better than proportional-integral-derivative control and mode-based proportional-derivative control in stability tracking performance and robustness. In addition, the CSPACE platform for rapid controller prototyping may reduce the arduous programming effort and offer a lot of ease for the trials.

Air-ground coordinated unmanned swarm systems: A multitasking framework for control design.

An air-ground heterogeneous unmanned swarm system coordination is considered. The system consists of N unmanned aerial vehicles (UAVs) and one unmanned ground vehicle (UGV). This forms a complicated mission, which consists of the following four different tasks. First, the aerial vehicles are in a compact formation, while avoiding collision with each other. Second, the aerial vehicles should stay close to the ground, while avoiding collision with the ground. Third, the aerial vehicles should stay close to the ground vehicle. Fourth, the ground vehicle should follow a desired trajectory. These tasks reflect two seemingly contradictory nature: close to (due to tracking) and away from (due to avoidance). The effective control design should address all four tasks even in the presence of uncertainty. By two creative transformations, this multitude of tasks are consolidated in a χ-measure. An adaptive robust control, which includes a robust control scheme and an online adaptation law, is then proposed to render guarantee boundedness performance of this χ-measure. As a result, the control design is able to accomplish the combined tracking-avoidance mission for the uncertain swarm system. Despite the presence of conflicting aspects between these tasks, the designed controller exhibits outstanding performance.

Adaptive Robust Formation Control of Connected and Autonomous Vehicle Swarm System Based on Constraint Following.

This article proposes an adaptive robust formation control scheme for the connected and autonomous vehicle (CAV) swarm system by utilizing swarm property, diffeomorphism transformation, and constraint following. The control design is processed by starting from a 2-D dynamics model with (possibly fast) time varying but bounded uncertainty. The uncertainty bounds are unknown. For compact formation, the CAV system is treated as an artificial swarm system, for which the ideal swarm performance is taken as a desired constraint. By this, formation control is converted into a problem of constraint following and then a performance measure ß is defined as the control object to evaluate the constraint following error. For collision avoidance, a diffeomorphism transformation on space measure between two vehicles is creatively performed, by which the space measure is positive restricted. For uncertainty handling, an adaptive robust control scheme is proposed to render the ß -measure to be uniformly bounded and uniformly ultimately bounded, that is, drive the controlled (CAV) swarm system to follow the desired constraint approximatively. As a result, the system can achieve the ideal swarm performance; thereout, compact formation is realized, regardless of the uncertainty. The main contribution of this article is exploring a 2-D formation control scheme for (CAV) swarm system under the consideration of collision avoidance and time-varying uncertainty.

Satellite Formation-Containment Control Emphasis on Collision Avoidance and Uncertainty Suppression.

This article explores an adaptive robust control scheme for satellite formation-containment flying in a way of constraint following. For safe flight and uncertainty suppression, both collision avoidance and uncertainty suppression are addressed. First, for uncertainty suppression, (possibly fast) time-varying but bounded uncertainty is considered, and then an adaptive law is proposed to estimate the comprehensive uncertainty bounds online. Second, the problem of formation-containment control with collision avoidance is converted into another problem of constraint-following control by taking the objectives of collision avoidance, formation, and containment, respectively, as the collision-avoidance constraint, formation constraint, and containment constraint. Third, an η -measure is introduced to gauge the constraint-following error, and then an adaptive robust control is proposed to render the error to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. By this, the satellites can follow the above collision-avoidance constraint, formation constraint, and containment constraint approximately. As a result, satellite formation-containment control emphasis on collision avoidance and uncertainty suppression is achieved.

High-order robust control and Stackelberg game-based optimization for uncertain fuzzy PMSM system with inequality constraints.

There exist the uncertainties and the inequality constraints in permanent magnet synchronous motor (PMSM) system. In order to meet the safety control requirements in industrial applications, the state transformation is used to meet the inequality constraints for limiting the outputs within desired bounds. Then, fuzzy set theory, which is different from fuzzy logic, is used to describe uncertainty, and the fuzzy PMSM dynamical model is established. Based on that, a robust control with high-order term is proposed to compensate for the time-varying uncertainty. Furthermore, for improving the system performance and decreasing the control cost, the Stackelberg game is introduced into the optimization scheme design, in which the leader plays a more important role than follower. These characteristic corresponds to the influence of the two tunable control parameters on the system. Thus, the optimal parameters are obtained by the rules of Stackelberg game. Finally, experimental results show the effectiveness of the above theories.

A Stackelberg Game-Theoretic Exploration Rendering Robustness and Optimality for Performance Improvement of Fuzzy Mechanical Systems.

We consider mechanical systems with uncertainty. The uncertainty may be time varying. The bound of the uncertainty is described by its fuzzy characteristics. To design a feasible control, we start with a robust phase, which renders a control scheme that guarantees the system performance regardless of the actual value of the uncertainty. This robust phase is then followed by an optimal phase. There are design parameters in the control, which can be fine-tuned. We proposed multiple performance objectives. The goal of the choice of the control design parameters is to minimize the performance objectives. However, since these objectives are nonconciliating (meaning one's minimum is not the other one's minimum), we invoke the Stackelberg strategy for the optimal parameters. The game strategy mimics two players: one is the leader and one is the follower. Through the interplay between the two players, we show how to select the design parameters. The design procedure in both robust and optimal phases is demonstrated by a coupled inverted pendulum system.

Regulating Constraint-Following Bound for Fuzzy Mechanical Systems: Indirect Robust Control and Fuzzy Optimal Design.

This article proposes an optimal indirect approach of constraint-following control for fuzzy mechanical systems. The system contains (possibly fast) time-varying uncertainty that lies in a fuzzy set. It aims at an optimal controller for the system to render bounded constraint-following error such that it can stay within a predetermined bound at all time and be sufficiently small eventually. First, for deterministic performance, the original system is transformed into a constructed system. A deterministic (not the usual IF-THEN rules-based) robust control is then designed for the constructed system to render it to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. Second, for optimal performance, a performance index, including the average fuzzy system performance and control effort, is proposed based on the fuzzy information. An optimal design problem associated with the control gain is then formulated and solved by minimizing the performance index. Finally, it is proved when the constructed system renders uniform boundedness and uniform ultimate boundedness, the original system achieves the desired performance of bounded constraint following.

Cooperative Game Approach to Robust Control Design for Fuzzy Dynamical Systems.

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

Optimal Design of High-Order Control for Fuzzy Dynamical Systems Based on the Cooperative Game Theory.

In this article, we propose a high-order robust control for fuzzy dynamical systems. The time varying but bounded uncertainty in this system is described by the fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. By the Lyapunov approach, we prove that the control is able to guarantee uniform boundedness and uniform ultimate boundedness. In addition, the tunable parameters in the high-order control are regarded as two players in a cooperative game. Two cost functions are also proposed based on the two players. These two cost functions are related to system performance and control cost. Then, the optimal design problem is solved by finding the Pareto-optimality parameters. Numerical simulations are performed for verification.

Robust Pointing Control of Marching Tank Gun With Matched and Mismatched Uncertainty.

This article focuses on a robust control scheme for pointing control of the marching tank gun. Both matched and mismatched uncertainties, which may be nonlinear (possibly fast) time varying but bounded, are considered. First, the pointing control system is constructed as a coupled, nonlinear, and uncertain dynamical system with two interconnected (horizontal and vertical) subsystems. Second, for the horizontal pointing control, robust control is proposed to render the horizontal subsystem to be practically stable. Third, for the vertical pointing control, an uncertainty bound-based state transformation is constructed in a similar way of backstepping to convert the original mismatched system (i.e., the vertical subsystem) to be locally matched and then robust control is proposed to render the transformed system to be practically stable. Finally, it is proved that when the transformed system is rendered to be practically stable, the original system renders the same performance; therefore, vertical pointing control is achieved. This work should be among the first ever endeavor to cast all the coupling, nonlinearity, and (both matched and mismatched) uncertainty into the pointing control framework of the marching tank gun.

Control Design With Optimization for Fuzzy Steering-by-Wire System Based on Nash Game Theory.

In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification.

Adaptive robust servo constraint tracking control for an underactuated quadrotor UAV with mismatched uncertainties.

In this research, to achieve the altitude and attitude tracking control of an underactuated quadrotor UAV with mismatched uncertainties, based upon Udwadia-Kalaba theory, a novel adaptive robust tracking control approach is proposed and which will be designed in two steps. First, aiming at the uncertain and underactuated quadrotor UAV, regardless of initial constraint deviation and mismatched uncertainties, a nominal control is constructed through transforming the desired trajectories into corresponding servo constraints; second, for the mismatched uncertainties, we decompose them into two parts, i.e. the matched part and mismatched part, and the mismatched part will "vanish" during the stability analysis of proposed adaptive robust controller. Eventually, with such a decomposition technique, the large mismatched uncertainties can be addressed properly and the burden of controller design will be reduced to a certain degree. In addition, two deterministic robust control performances are also guaranteed by our proposed approach. The simulation results have shown a good robustness and tracking precision of our proposed scheme for quadrotor UAV.

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 levitation control for maglev systems with guaranteed bounded airgap.

The robust control design problem for the levitation control of a nonlinear uncertain maglev system is considered. The uncertainty is (possibly) fast time-varying. The system has magnitude limitation on the airgap between the suspended chassis and the guideway in order to prevent undesirable contact. Furthermore, the (global) matching condition is not satisfied. After a three-step state transformation, a robust control scheme for the maglev vehicle is proposed, which is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system, regardless of the uncertainty. The magnitude limitation of the airgap is guaranteed, regardless of the uncertainty.