Nonsingular Practical Fixed-Time Adaptive Output Feedback Control of MIMO Nonlinear Systems

Adaptive fixed-time fuzzy containment control for uncertain nonlinear multiagent systems with unmeasurable states

This paper addresses the adaptive fixed-time fuzzy containment control for uncertain nonlinear multiagent systems, where the states and nonlinear functions are not feasible for the controller design. To address the issue of unmeasurable states, a state observer is developed, and fuzzy logic systems are utilized to approximate unknown nonlinear functions. Under the framework of fixed-time Lyapunov function theory and cooperative control, an adaptive fixed-time fuzzy containment control protocol is derived via the adaptive backstepping and adding one power integrator method. The derived fixed-time containment controller can confirm that the closed-loop systems are practical fixed-time stable, which implies that all signals in the systems are bounded and all follower agents can converge to the convex hull formed by the leader agents within fixed-time in the presence of unmeasurable states and unknown nonlinear functions . Simulation examples are conducted to test the validity of the present control algorithm.

Bionic Swarm Control Based on Second-Order Communication Topology

In this article, we propose bionic swarm control based on second-order communication topology (SOCT) inspired by the migration of birds, which solves the difficulty in constructing communication topologies and high-computational complexity in controlling large-scale swarm systems. To realize bionic swarm control, there are three problems supposed to be solved. First, the adjacency matrix and the Laplacian matrix in traditional methods cannot be applied to SOCT directly, which should be redesigned. Second, sub-swarm systems formed based on 2-order communication topology (2-OCT) and independently distributed with each other also need to be put forward to reduce computational complexity. At last, the followers in 1-order communication topology (1-OCT) are set as the leaders of sub-swarm systems in 2-OCT. As a result, coupling in large-scale swarm systems would be reduced. The bionic swarm controller is designed through the backstepping method. In this case, the stability of bionic swarm controller is proven by the designed Lyapunov function. The simulations show the efficiency of the designed bionic swarm controller. And the tracking-containment control based on SOCT with 42 swarm members is realized.

Practical discontinuous tracking control for a permanent magnet synchronous motor

In this paper, the practical discontinuous control algorithm is used in the tracking controller design for a permanent magnet synchronous motor (PMSM). Although the theory of discontinuous control has been studied intensely, it is seldom applied to the actual systems, which encourages us to spread the discontinuous control algorithm to motor control. Due to the constraints of physical conditions, the input of the system is limited. Hence, we design the practical discontinuous control algorithm for PMSM with input saturation. To achieve the tracking control of PMSM, we define the error variables of the tracking control, and the sliding mode control method is introduced to complete the design of the discontinuous controller. Based on the Lyapunov stability theory, the error variables are guaranteed to converge to zero asymptotically, and the tracking control of the system is realized. Finally, the validity of the proposed control method is verified by a simulation example and the experimental platform.

Game-Based Backstepping Design for Strict-Feedback Nonlinear Multi-Agent Systems Based on Reinforcement Learning

In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

Distributed adaptive fixed-time neural networks control for nonaffine nonlinear multiagent systems

This paper, with the adaptive backstepping technique, presents a novel fixed-time neural networks leader–follower consensus tracking control scheme for a class of nonaffine nonlinear multiagent systems. The expression of the error system is derived, based on homeomorphism mapping theory, to formulate a set of distributed adaptive backstepping neural networks controllers. The weights of the neural networks controllers are trained, by an adaptive law based on fixed-time theory, to determine the adaptive control input. The control algorithm can guarantee that the output of the follower agents of the system effectively follow the output of the leader of the system in a fixed time, while the upper bound of the settling time can be calculated without initial parameters. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed consensus tracking control approach. A step-by-step procedure for engineers and researchers interested in applications is proposed.