Full-Order Sliding Mode Bounded Control for Euler-Lagrange Systems with External Disturbances

This paper researches two finite-time bounded control methods for Euler-Lagrange systems exposed to external disturbances. A novel full-order terminal sliding mode surface that is convenient for solving the input constraints is designed based on the characters of the hyperbolic tangent function. By using the designed full-order terminal sliding mode surface, the finite-time controller with input constraints can deal with external disturbances with the exactly known upper bound. Further, an adaptive finite-time bounded controller is designed to deal with the external disturbances with the upper bound that cannot be accurately known. Finally, the finite-time stability of the system is proved by using Lyapunov theory and numerical simulations.

The Stability of the Systems with Command Saturation, Command Delay, and State Delay

This article presents the study of the stability of single-input and multiple-input systems with point or distributed state delay and input delay and input saturation. By a linear transformation applied to the initial system with delay, a system is obtained without delay, but which is equivalent from the point of view of stability. Next, using sufficient conditions for the global asymptotic stability of linear systems with bounded control, new sufficient conditions are obtained for global asymptotic stability of the initial system with state delay and input delay and input saturation. In addition, the article presents the results on the instability and estimation of the stability region of the delay and input saturation system. The numerical simulations confirming the results obtained on stability were performed in the MATLAB/Simulink environment. A method is also presented for solving a transcendental matrix equation that results from the process of equating the stability of the systems with and without delay, a method which is based on the computational intelligence, namely, the Particle Swarm Optimization (PSO) method.

Velocity-free attitude tracking for rigid spacecraft via bounded control

This article investigates the attitude tracking control problem for a rigid spacecraft without angular velocity feedback, in which external disturbances, parametric uncertainties, and input saturation are considered. Initially, an angular velocity observer is developed incorporated with adaptive technique, which could tackle the unmeasurable angular velocity and system uncertainties simultaneously. By introducing adaptive updating law into the proposed observer, the synchronized uncertainties are handled such that robustness of the observer is enhanced, even in the presence of external disturbances. Further, for solving the input constraints problem, command filter and backstepping method are utilized; thus, a bounded attitude tracking control law is derived. Finally, the attitude tracking performance is evaluated by numerical examples.

Super-twisting disturbance observer–based fuzzy adaptive finite-time control for a class of space unmanned systems with time-varying output constraints

In practical flight process, the time-varying disturbances are often encountered by the space unmanned systems, and the attitude outputs of the space unmanned systems are required to stay in the predefined intervals. Moreover, the convergence process of the space unmanned systems has to be achieved in finite time, to complete the given tasks. However, most of the existing results are difficult to be applied to give consideration to the finite-time-convergence, the constrained outputs and the suppression for the time-varying disturbances simultaneously. To address this problem, in this article, we propose a novel fuzzy adaptive finite-time anti-disturbance control scheme for the space unmanned systems. The super-twisting disturbance observer, which possess the robust and finite-time disturbance estimation ability, has been utilized to suppress the time-varying disturbances. The nonlinear signal transformation technique has been introduced, transforming the constrained outputs into a novel unconstrained auxiliary variable, and the output constrained control issue becomes an equivalent bounded control problem. To achieve the finite-time convenience of the closed-loop space unmanned system, the fractional control laws have been designed, and an important lemma has been utilized to design the update laws of the adaptive parameters. Moreover, the fuzzy logic systems have been used to improve the robustness respect to the uncertainties. The contrastive simulation results have been provided, the finite-time control ability of the proposed method and the satisfactory estimation performance of the super-twisting disturbance observer can be observed.

Bounded finite-time stabilization of the prey – predator model via Korobov’s controllability function

The problem of finite-time stabilization for a Leslie-Gower prey – predator system through a bounded control input is solved. We use Korobov’s controllability function. The trajectory of the resulting motion is ensured for fulfilling a physical restriction that prey and predator cannot achieve negative values. For this purpose, a certain ellipse depending on given data and the equilibrium point of the considered system is constructed. Simulation results show the effectiveness of the proposed control methodology.

Collision Avoidance of a Kinodynamically Constrained System from Passive Agents

Robot motion planning in dynamic environments is significantly difficult, especially when the future trajectories of dynamic obstacles are only predictable over a short time interval and can change frequently. Moreover, a robot’s kinodynamic constraints make the task more challenging. This paper proposes a novel collision avoidance scheme for navigating a kinodynamically constrained robot among multiple passive agents with partially predictable behavior. For this purpose, this paper presents a new approach that maps collision avoidance and kinodynamic constraints on robot motion as geometrical bounds of its control space. This was achieved by extending the concept of nonlinear velocity obstacles to incorporate the robot’s kinodynamic constraints. The proposed concept of bounded control space was used to design a collision avoidance strategy for a car-like robot by employing a predict-plan-act framework. The results of simulated experiments demonstrate the effectiveness of the proposed algorithm when compared to existing velocity obstacle based approaches.

Optimal Control and Positional Controllability in a One-Sector Economy

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.