Adaptive robust control for fuzzy underactuated mechanical systems: A Stackelberg game-theoretic optimization approach

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.

For general uncertain nonlinear time-delay systems, a domination design approach to robust adaptive controller based on Lyapunov-Razumikhin function is provided. To deal with the obstacle brought by the Lyapunov-Razumikhin function with the Razumikhin condition, a new parameter variable is introduced into the adaptive controller design instead of the conventional parameter variable. Based on Lyapunov-Razumikhin stability theory, it is shown that the proposed robust adaptive controller can guarantee the global uniform ultimate boundedness of all the signals in the resulting closed-loop dynamical system. In addition, it is also shown that the proposed design scheme can be applied to recursive design for the robust adaptive stabilizing controller of general uncertain nonlinear time-delay systems with triangular structure.

Design of an adaptive controller for complex dynamic systems is a big challenge faced by the researchers. In this paper, we propose a novel method for the design of an error- based robust adaptive controller to make the system response reasonably fast with no overshoot. Here the control action is designed by introducing the notion of ‘error-based adaptive controller’ (EB-AC). In the design of this feedback adaptive controller, parameters of the controller are designed as a function of the system error. For example, the position feedback parameter K p (e, t), which controls the bandwidth of the system as well as the dynamic response, is a function of the system error e(t). In the design of the position feedback parameter K p (e, t), for large error K p (e, t) is kept large, thus increasing the bandwidth of the system which yields a fast response, whereas for decreasing errors, K p (e, t) is continuously decreased to a small value. Thus, during the dynamic response of the system, the bandwidth of the system is continuously controlled by the system error e(t). Similarly, the velocity feedback parameter K v (e, t) which controls the damping of the system is kept very small for large errors, and continuously increased to a large value for decreasing value of error. Hence, in the design of the proposed adaptive controller, the position feedback K p (e, t) and the velocity feedback K v (e, t) are formulated as a function of the system error, and this approach for formulating the adaptive controller yields a very fast response with no overshoot. In this paper, we present an error-based robust adaptive control design methodology for a linear system.

In order to ensure the safety and stability of vehicle platoons, the spacing error between vehicles needs to be maintained within a given range and gradually converge to 0. Due to actuator saturations and time-varying uncertainties in vehicle dynamics, the vehicle platoon control remains a major challenge. This paper presents a robust control method for vehicle platoons, ensuring the spacing error performance within a compact prescribed band region. Firstly, an improved spacing modeling method is presented, embedded with an auxiliary variable to modify the spacing error. It effectively circumvents actuator saturations caused by excessively large initial errors. Then, bilateral constraints are imposed on the modified error to characterize collision avoidance and compact formation (CA&CF) performance, and subsequently the constrained error is transformed into an unconstrained state via potential function transformation. The uniform boundedness (UB) performance of the unconstrained state ensures the compact prescribed band region performance of the spacing error. Then, based on the constraint-following control theory, a robust controller is designed to ensure the system’s UB and uniform ultimate boundedness (UUB) performance. Finally, simulation results demonstrate the effectiveness of the proposed control.

The design of a new hybrid controller for fractional-order uncertain chaotic systems with unknown time-varying delays

This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.

Robust adaptive boundary control of a flexible marine riser with vessel dynamics

Underactuated systems are mechanical systems with fewer actuators than the system degrees of freedom, i.e., some degrees of freedom are not directly driven by actuators. Many benchmark underactuated systems have been developed to study the nature of underactuated dynamics and their possible controller designs. Unlike fully actuated systems where many control strategies are available for an entire class of systems, there are few results applicable to even a small class of underactuated mechanical systems. In this paper, an Adaptive Fuzzy Sliding Mode Controller (AFSMC) is proposed in order to stabilize an inverted pendulum mounted on a ball system, also known as ballbot; this latter an interesting underactuated mechanical system for which the controller designs are a pending task, i.e. the performance for different control strategies could be explored. The performance of our proposal is verified via numerical simulation, showing the robustness against time-varying uncertainties and disturbances.

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L 2 tracking performance to stabilise the closed-loop system. This L 2 tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.

The management of uncertainty and inequality constraint is essential for the high-speed and high-precision motion control of a permanent magnet linear motor (PMLM). This article develops a robust control with a dual-parameters optimization for the constrained PMLM system. The uncertainties considered in this article, including parameter uncertainties and external disturbances, are bounded within prescribed fuzzy sets. The tracking error is desired to maintain within a specified range (i.e., the inequality constraint) due to the limited travel range and the demand for bounded tracking performance of the PMLM system. By employing a state transformation, the bounded state is converted into an unbounded one. Therefore, the inequality constraint is creatively integrated into the trajectory tracking control problem. Based on the transformed system, an optimal robust control is established which can be divided into two steps. First, a deterministic robust control is proposed which guarantees the practical stability: uniform boundedness and uniform ultimate boundedness. Second, a two-player Stackelberg game is formulated to seek the optimal control parameters. The cost function of each player in the game reflects both the control performance and the control cost such that the tradeoff problem between the two conflicting criteria is further clarified. Finally, experimental results demonstrate the superior performance of the proposed optimal robust control over two existing control schemes.

This paper considers the cooperative control problem for the unmanned ground vehicle swarm system with cyber interference. Each vehicle in the system is intelligent and connected with each other via networks. The cyber security issue is inevitable and vital in the control design for the swarm system. Taking account of the cyber interference and system uncertainty, we explore the cooperative control for the unmanned ground vehicle swarm system. In order to describe the behaviors of mutual attraction, repulsion and overall trajectory tracking in a mathematical manner, we abstract the integrated potential function, thereby the kinematic model. Treating the mathematical model as the system constraint and decomposing the system uncertainty, we propose a class of cooperative adaptive robust controls to assure that all the unmanned ground vehicles follow the constraint to move. Four major system performances are achieved: (i) global stability (i.e., uniform boundedness and uniform ultimate boundedness), (ii) compact formation, (iii) cooperative hunting, (iv) trajectory tracking.

Hydraulic system is widely used in industry where large actuation forces are needed such as electro-hydraulic positioning system, active suspension control, and so on. One of the main problem in hydraulic system is the nontriviality, for instance, the deadbands in valve operation, frictions of links, saturations, pressure dynamics, etc. both system unknown nonlinearities and external disturbances should be considered in controller design. For underwater hydraulic manipulator, because of the environment of sea and the large nonlinearities of the hydraulic manipulator system, both system unknown nonlinearities and external disturbances should be considered in controller design. A lot of control methods have been proposed to solve the problem properly, such as sliding mode control, adaptive control, fuzzy adaptive control, adaptive robust control, ect. However, due to limited knowledge about hydraulic manipulator system, it is hard to precisely estimate the nonlinearities for a possible higher performance. In this paper, a neural network adaptive robust control method is proposed to help control an underwater hydraulic manipulator. In order to achieve better performance using adaptive robust control strategy, unknown nonlinearities in the system are approximated by the outputs of radial basis function neural network (RBFNNs). A projection law has been used to bound the NN weights when they are tuning on-line to avoid possible adaptive divergence, and the tracking transient performance is guaranteed by robust control law. Simulation results illustrate that manipulator has a good tracking performance.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

A robust adaptive neural network control approach is presented for a class of uncertain strict-feedback nonlinear systems with unknown dead-zone and disturbances. In the controller design, a single neural network is used to approximate the lumped unknown part of the system. By the approach, only one actual control law is implemented at the last step, and all the virtual control laws at intermediate steps need not be implemented actually. Thus, the designed controller is simpler in structure. Furthermore, the actual control law and one adaptive law can be given directly for the class of systems under study. The result of stability analysis shows that the proposed scheme can guarantee the uniform ultimate boundedness of all the closed-loop system signals, and the steady-state tracking error can be made arbitrarily small by appropriately choosing control parameters. A simulation example is given to demonstrate the effectiveness and merits of the proposed approach.

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.