In this article, to address the issue of accelerating convergence performance and eliminating the tracking error, an advanced optimal control method for nonlinear discrete-time systems is investigated based on an improved N-step [( ${N} +1$ )-step] gradient learning algorithm. Independent of the discount factor, this article introduces a novel tracking error index without quadratic input terms for the steady-state and convergence performances, which obtains the optimal control policy without calculating the reference control input. Compared with classic N-step gradient learning algorithms with infinite future reward assumption, the proposed algorithm investigates the (N +1)-step return with a fixed N and a step forward for finite tracking problems based on a long-term weighting parameter. Based on the above theory, value iteration (VI) and policy iteration (PI) methods are utilized to derive the convergence, monotonicity, optimality, and stability properties of the proposed algorithm, which can be conducted without the traditional assumption of zero initial functions. In the implementation of the algorithms, the actor-critic structure, constructed by four neural networks, is established to approximate the states, the value functions, and the control policy, respectively. Three simulation experiments on a helicopter system validate the efficacy and practicality of the control methods in addressing nonlinear optimal tracking challenges.

Addressing external disturbances has been a critical issue for control design to ensure reliable operation of systems. This article investigates the tracking control problem for the uncertain nonlinear systems with the strong external disturbance and the prescribed performance. The flexible performance-based control scheme is developed by introducing an external disturbance criterion into the prescribed performance. It is capable of guaranteeing the prescribed performance if the external disturbance is less than a specified threshold and degrading that in light of the user-appointed rule otherwise. Particularly, the disturbance interval observer is synthesized to generate the boundaries of the external disturbances and realize the judgment of that criterion. With the generated boundaries, the interval-type auxiliary system is designed to provide the modified performance functions (MPFs) that characterize performance requirement and degradation rule simultaneously. Based on the positive system theory and the Lyapunov method, it is theoretically shown that the system output can always track the reference signal and satisfy the constraints of MPFs. Finally, both the numerical simulation and the application of flight control design verify that the results are effective and valid.

In this article, a disturbance-observer-based adaptive fuzzy tracking control scheme is proposed for a medium-scale unmanned helicopter of six degrees of freedom in the presence of system uncertainties, flight boundary constraints, and external disturbances. A flight boundary protection algorithm is proposed to ensure its flight trajectory within the given safety range. A fuzzy logic system is utilized to estimate the system uncertainties and a nonlinear disturbance observer is adopted to handle the unknown compound terms of the external disturbances and the estimation errors resulting from the fuzzy logic system. An inverse optimal control approach is then used to avoid solving the Hamilton–Jacobi–Bellman equation in minimizing a cost function in the attitude loop. It is shown via the Lyapunov method that the desired safe tracking performance of the position loop and attitude loop of the controlled unmanned helicopter can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

In this article, an adaptive neural safe tracking control scheme is studied for a class of uncertain nonlinear systems with output constraints and unknown external disturbances. To allow the output to stay in the desired output constraints, a boundary protection approach is developed and utilized in the output constrained problem. Since the generated output constraint trajectory is piecewise differentiable, a dynamic surface method is utilized to handle it. For the purpose of approximating the system uncertainties, a radial basis function neural network (RBFNN) is adopted. Under the output of the RBFNN, the disturbance observer technology is employed to estimate the unknown compound disturbances of the system. Finally, the Lyapunov function method is utilized to analyze the convergence of the tracking error. Taking a two-link manipulator system, as an example, the simulation results are presented to illustrate the feasibility of the proposed control scheme.

In this article, an adaptive neural fault-tolerant control (FTC) scheme is proposed for the medium-scale unmanned autonomous helicopter subject to external disturbance, actuator fault, and input saturation. Multiple approximators are constructed to handle the unknown terms and promote the control design. The nonlinear coupled function terms are approximated by virtue of the radial basis function neural networks. The unknown disturbance is tackled by the developed disturbance observer. Meanwhile, two auxiliary systems are introduced to handle the actuator fault and input saturation, respectively. In the framework of the backstepping method, a multiapproximator-based adaptive FTC strategy is presented, which assures the boundedness of all closed-loop system signals. Simulation results are presented to validate the availability of the designed controller.

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

In this paper, a tracking flight control scheme is proposed based on a disturbance observer for a quadrotor with external disturbances. To facilitate the processing of external time-varying disturbances, it is assumed to consist of some harmonic disturbances. Then, a disturbance observer is proposed to estimate the unknown disturbance. By using the output of the disturbance observer, a flight controller of the quadrotor is developed to track the given signals which are generated by the reference model. Finally, the proposed control method is applied to flight control of the quadrotor Quanser Qball 2. The experimental results are presented to demonstrate the effectiveness of the developed control strategy.

A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.