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This paper presents a data-based robust adaptive control methodology for a class of nonlinear constrained-input systems with completely unknown dynamics. By introducing a value function for the nominal system, the robust control problem is transformed into a constrained optimal control problem. Due to the unavailability of system dynamics, a data-based integral reinforcement learning (RL) algorithm is developed to solve the constrained optimal control problem. Based on the present algorithm, the value function and the control policy can be updated simultaneously using only system data. The convergence of the developed algorithm is proved via an established equivalence relationship. To implement the integral RL algorithm, an actor neural network (NN) and a critic NN are separately utilized to approximate the control policy and the value function, and the least squares method is employed to estimate the unknown parameters. By using Lyapunov's direct method, the obtained approximate optimal control is verified to guarantee the unknown nonlinear system to be stable in the sense of uniform ultimate boundedness. Two examples are provided to demonstrate the effectiveness and applicability of the theoretical results.

In this paper, the robust optimal control of continuous-time affine nonlinear systems with matched uncertainties is investigated by using a data-based integral policy iteration approach. It is a natural extension of the traditional optimal control design, under the framework of adaptive dynamic programming (ADP) method, to robust optimal control of nonlinear systems with matched uncertainties. In theoretical aspect, by increasing a feedback gain to the optimal controller of the nominal system, the robust controller of the matched uncertain system is obtained, which also achieves optimality with a newly well-defined cost function. When regarding the implementation, the data-based integral policy iteration algorithm is used to solve the Hamilton-Jacobi-Bellman equation corresponding to the nominal system with completely unknown dynamics information. Then, the actor-critic technique based on neural networks and least squares implementation method are employed to facilitate deriving the optimal control law iteratively, so that the closed-form expression of the robust optimal controller is available. Additionally, two simulation examples with application backgrounds are presented to illustrate the effectiveness of the established robust optimal control scheme. In summary, it is important to note that the result developed in this paper broadens the application scope of ADP-based optimal control approach to more general nonlinear systems possessing dynamical uncertainties.

In this paper, the neural-network-based robust optimal control design for a class of uncertain nonlinear systems via adaptive dynamic programming approach is investigated. First, the robust controller of the original uncertain system is derived by adding a feedback gain to the optimal controller of the nominal system. It is also shown that this robust controller can achieve optimality under a specified cost function, which serves as the basic idea of the robust optimal control design. Then, a critic network is constructed to solve the Hamilton-Jacobi-Bellman equation corresponding to the nominal system, where an additional stabilizing term is introduced to verify the stability. The uniform ultimate boundedness of the closed-loop system is also proved by using the Lyapunov approach. Moreover, the obtained results are extended to solve decentralized optimal control problem of continuous-time nonlinear interconnected large-scale systems. Finally, two simulation examples are presented to illustrate the effectiveness of the established control scheme.

In the previous work of Huang et al., a decentralized direct adaptive fuzzy H"~ tracking controller of large-scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable. In this note, we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller. By combination of a state observer, a fuzzy inference system and robust control technique, the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required. All the signals of the closed-loop large-scale system are proved to be uniformly ultimately bounded. The effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums.

This paper proposes a novel dynamic structure neural fuzzy network (DSNFN) to address the adaptive tracking problems of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. The proposed control scheme uses a four-layer neural fuzzy network (NFN) to estimate system uncertainties online. The main feature of this DSNFN is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors. Projection-type adaptation laws for the network parameters are derived from the Lyapunov synthesis approach to ensure network convergence and stable control. A hybrid control scheme that combines the sliding-mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors. As the employment of the DSNFN, high-quality tracking performance could be achieved in the system. Furthermore, the trained network avoids the problems of overfitting and underfitting. Simulations performed on a two-link robot manipulator demonstrate the effectiveness of the proposed control scheme.

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.

We utilize optimization algorithms inspired by the immune system for treating the mixed H"2/H"~ control problem. Both precisely known systems and uncertain systems with polytopic uncertainties are investigated. For the latter, a novel methodology is proposed to compute the worst case norms within the polytope of matrices. This methodology consists in defining the worst case norm computation as an implicit optimization problem with a special structure. We exploit this structure of the problem for its solution. The paper presents both mono and multiobjective optimization algorithms developed from the clonal selection principle. The former is the real-coded clonal selection algorithm (RCSA) and the latter is the multiobjective clonal selection algorithm (MOCSA). The complete design process involves the combination of synthesis and analysis. The RCSA is used for analysis, through the worst case norm computation for a given provided controller. The MOCSA is used for synthesis, working on a population of candidate controllers, until providing an estimate of the Pareto set for the mixed H"2/H"~ control problem. The numerical examples illustrate the power and the validity of the proposed approach for robust control design. Moreover, our approach for worst case norm evaluation is compared with other approaches available in literature.

This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach.

In order to cope with parametric uncertainties of nonlinear systems, a numerical analysis method of a robust feedback linearization control scheme based on fuzzy models is proposed. The fuzzy feedback linearization control scheme ensures that the control operates stably under bounded parametric uncertainties. For the system with known uncertainty bounds, linear matrix inequality based robust stability condition is derived and a robust fuzzy feedback linearization regulators can be designed by choosing the control parameters satisfying the inequalities which give sufficient conditions for the closed loop system to be stable. To verify the validity and effectiveness of the designed stability analysis methods, the suggested analysis techniques are applied to a balancing control of inverted pendulum systems.