A novel robust adaptive controller for multi-input multi-output (MIMO) feedback linearizable nonlinear systems possessing unknown nonlinearities, capable of guaranteeing a prescribed performance, is ...developed in this paper. By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. Visualizing the prescribed performance characteristics as tracking error constraints, the key idea is to transform the ldquoconstrainedrdquo system into an equivalent ldquounconstrainedrdquo one, via an appropriately defined output error transformation. It is shown that stabilization of the ldquounconstrainedrdquo system is sufficient to solve the stated problem. Besides guaranteeing a uniform ultimate boundedness property for the transformed output error and the uniform boundedness for all other signals in the closed loop, the proposed robust adaptive controller is smooth with easily selected parameter values and successfully bypasses the loss of controllability issue. Simulation results on a two-link robot, clarify and verify the approach.
Numerous tasks in control systems involve optimization problems over polynomials, and unfortunately these problems are in general nonconvex. In order to cope with this difficulty, linear matrix ...inequality (LMI) techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems. This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Pólya's theorem, and matrix dilation. Moreover, it aims to provide a collection of the essential problems in control systems where these LMI techniques are used, such as stability and performance investigations in nonlinear systems, uncertain systems, time-delay systems, and genetic regulatory networks. It is expected that this survey may be a concise useful reference for all readers.
This study is concerned with the control problem of networked non-linear systems with communication delay and data dropout. A networked non-linear predictive control scheme is proposed to compensate ...for communication delay and data dropout actively rather than passively. The stability analysis shows that the stability problem of the closed-loop networked non-linear predictive control system is converted to the one of a conventional non-linear control system without network. The simulations illustrate that the proposed scheme can compensate for communication delay and data dropout, and achieve the same control performance of the local closed-loop control system without network.
•Model-free VRFT applied to ADRC combined with fuzzy control is proposed.•Least-squares algorithm specific to VRFT is replaced with Grey Wolf Optimizer.•The fuzzy control system stability is employed ...in the design approaches.•Model-free optimal tuning of controllers for tower crane systems is done.•Experimentally validated model-free controllers are offered.
This paper proposes the Virtual Reference Feedback Tuning (VRFT) of a combination of two control algorithms, Active Disturbance Rejection Control (ADRC) as a representative data-driven (or model-free) control algorithm and fuzzy control, in order to exploit the advantages of data-driven control and fuzzy control. The combination of Active Disturbance Rejection Control with Proportional-Derivative Takagi-Sugeno Fuzzy Control (PDTSFC) tuned by Virtual Reference Feedback Tuning results in two novel data-driven algorithms referred to as hybrid data-driven fuzzy ADRC algorithms. The main benefit of this combination is the automatic optimal tuning in a model-free manner of the parameters of the combination of Active Disturbance Rejection Control with Proportional-Derivative Takagi-Sugeno Fuzzy Control called ADRC-PDTSFC. The second benefit is that the suggested combination is time saving in finding the optimal parameters of the controllers. However, since Virtual Reference Feedback Tuning generally works with linear controllers to solve a certain optimization problem and the fuzzy controllers are essentially nonlinear, this paper replaces the least-squares algorithm specific to Virtual Reference Feedback Tuning with a metaheuristic optimization algorithm, i.e. Grey Wolf Optimizer. The fuzzy control system stability is guaranteed by including a limit cycle-based stability analysis approach in Grey Wolf Optimizer algorithm to validate the next solution candidates. The hybrid data-driven fuzzy ADRC algorithms are validated as controllers in terms of real-time experiments conducted on three-degree-of-freedom tower crane system laboratory equipment. To determine the efficiency of the new hybrid data-driven fuzzy ADRC algorithms, their performance is compared experimentally with that of two control algorithms, namely Active Disturbance Rejection Control with Proportional-Derivative Takagi-Sugeno Fuzzy Control, whose parameters are optimally tuned by Grey Wolf Optimizer in a model-based manner using the nonlinear process model.
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A universal, approximation-free state feedback control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed ...performance and bounded closed loop signals. By prescribed performance, it is meant that the output error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, having maximum overshoot less than a preassigned level. The proposed state feedback controller isolates the aforementioned output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties, while completely avoiding the explosion of complexity issue raised by backstepping-like approaches that are typically employed to the control of pure feedback systems. In this respect, a low complexity design is achieved. Moreover, the controllability assumptions reported in the relevant literature are further relaxed, thus enlarging the class of pure feedback systems that can be considered. Finally, simulation studies clarify and verify the approach.
This paper focuses on the problem of modeling and adaptive tracking for a class of stochastic Lagrangian control systems with unknown parameters. By reasonably introducing random noise, a method to ...construct stochastic Lagrangian control systems is given. Under some milder assumptions, an adaptive tracking controller is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The reasonability of assumptions and the efficiency of the controller are demonstrated by a mechanics model in random vibration environment.
It is both theoretically and practically important to investigate the problem of accommodating infinite number of actuator failures or faults in controlling uncertain systems. However, there is still ...no result available in developing adaptive controllers to address this problem. In this paper, a new adaptive failure/fault compensation control scheme is proposed for parametric strict feedback nonlinear systems. The techniques of nonlinear damping and parameter projection are employed in the design of controllers and parameter estimators, respectively. It is proved that the boundedness of all closed-loop signals can still be ensured in the case with infinite number of failures or faults, provided that the time interval between two successive changes of failure/fault pattern is bounded below by an arbitrary positive number. The performance of the tracking error in the mean square sense with respect to the frequency of failure/fault pattern changes is also established. Moreover, asymptotic tracking can be achieved when the total number of failures and faults is finite.
This paper proposes a method to overcome the singularity problem of terminal sliding-mode control systems. The system behaviors in both the reaching phase and the ideal sliding-mode are analyzed. A ...global nonsingular terminal sliding-mode control strategy for nonlinear systems is developed and it is shown that the proposed control strategy can eliminate the singularity, while guaranteeing the finite-time reachability of the systems to the terminal sliding-mode surface and the finite-time convergence of the systems towards the origin along the terminal sliding-mode surface.
This paper presents control design for strict feedback nonlinear systems with time-varying output constraints. An asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to ensure ...constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. Through a change of tracking error coordinates, we eliminate the explicit dependence of the BLF on time, thereby simplifying the analysis of constraint satisfaction. We show that asymptotic output tracking is achieved without violation of the output constraint, and also quantify the transient performance bound as a function of time that converges to zero. To handle parametric model uncertainty, we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation. The performance of the proposed control is illustrated through a simulation example.
We consider the tracking problem of unknown, robustly stabilizable, multi-input multi-output (MIMO), affine in the control, nonlinear systems with guaranteed prescribed performance. By prescribed ...performance we mean that the tracking error converges to a predefined arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants. Utilizing an output error transformation, we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system, provided that initially the transformed system is well defined. Consequently, a switching robust control Lyapunov function (RCLF)-based adaptive, state feedback controller is designed, to solve the stated problem. The proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable. Simulations illustrate the approach.
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