This study presents a self-triggered distributed model predictive control algorithm for the flock of a multi-agent system. All the agents in a flock are endowed with the capability of determining the sampling time adaptively to reduce the unnecessary energy consumption in communication and control updates. The agents are dynamically decoupled in a flock, and each agent is driven by a local model predictive controller, which is designed by minimising the position irregularity between the agent and its neighbours, velocity tracking errors as well as its control efforts. Moreover, the collision avoidance is considered by introducing constraints in the model predictive minimisation problem. In order to adaptively determine the sampling time, a self-triggered algorithm is designed by guaranteeing the decrease of the Lyapunov function. Finally, numerical simulations are given to demonstrate the feasibility of the proposed flocking algorithm.

This study establishes an approximate optimal critic learning algorithm based on single-network adaptive dynamic programming aiming at solutions to continuous-time two-player zero-sum games in the absence of initial stabilising control policies. Single-network means one critic neural network, which is utilised to derive the saddle-point equilibrium of a zero-sum differential game by approximately learning the value function. First, the authors elaborate mathematically two-player zero-sum game problems and analyse the similarity of the zero-sum game problem between linear and non-linear systems. Then, this adaptive learning scheme is implemented as a critic structure that derives control and disturbance policies by learning the optimal value, and a novel weight tuning law involving a stable operator is proposed to ensure convergence and stability. Moreover, the uniform ultimate bounded stability of the whole system is rigorously proved by Lyapunov theory. Finally, reasonable simulation results are provided to confirm the effectiveness of the improved approximate optimal control technique in solving equations for a complex linear system and a non-linear system.

In this study, a composite robust control approach with non-singular terminal sliding mode control and fixed-time disturbance observer (FxTDO) is proposed for a class of second-order non-linear systems in the presence of matched uncertain disturbances. A bi-limit-weighted homogeneous FxTDO is designed based on the efficient utilisation of power functions obtained by the differentiation error amplification strategy. The FxTDO enjoys a fast convergence rate and simple parameters tuning process. By introducing the disturbance estimation to directly compensate the total disturbance in the composite control law, only a particular small gain-based discontinuous control term is needed to guarantee the existence of sliding mode, and chattering phenomenon can be attenuated. The simulation results revealed the effectiveness of the proposed method.

This study proposes a novel multi-rate model predictive control (MPC) scheme for linear discrete-time systems subject to input constraints. The proposed scheme consists of two control layers, acting at two different timescales. At a slow timescale, the outputs associated with the slow dynamics are steered to their reference values while at a fast timescale, a shrinking horizon MPC regulator is designed to refine the control action computed at the slow timescale. The proposed control scheme shows to be particularly useful, not only to control systems with different open-loop dynamics but also in cases when the controlled variables are required to have different responsiveness in a closed loop. Simulation results on a fire tube boiler example are reported, which indeed show that different dynamics can be efficiently imposed on the controlled variables, i.e. the boiler pressure and the water level, in the presence of variations of the disturbance represented by the steam output flow rate.

An improved frequency-domain method for the fractional order controller design is proposed in this study. A proportional relation between the integral gain and derivative gain of the controller is built, while the derivative order is set to be equal to the integral order. Applying the improved method, the controller parameters can be calculated analytically according to different design requirements. The proportional coefficient between the integral and derivative gains is studied and then the model of the optimal proportional coefficient for the commonly used permanent magnet synchronous motor speed control system is built. Based on the established model, the optimal controllers are obtained analytically applying the proposed method. Motor speed control simulations and experiments are performed, comparing the performance of the controllers obtained using the proposed method and those obtained using the current frequency-domain method and other design methods. Simulation and experimental results show that the control system obtained using the proposed method achieves the specified stability, robustness to gain variations and the optimal dynamic performance.