This paper investigates the problem of safety-critical multi-tasks control (SCMTC) for switched systems, where the multi-tasks control is achieved by ensuring the invariance and attraction of the task set. A new definition of safety is presented under the switched systems framework, which extends the existing safety definition for non-switched systems and reveals the essence of safety for switched systems. For two different types of task sets, a single barrier function (SBF) method and a multiple barrier functions method are proposed to solve the SCMTC problem, where the former requires each task set to be defined by a continuously differentiable function, while the latter requires that to be defined by multiple continuously differentiable functions. Both the two methods allow the safety and/or the invariance and attraction of the task sets to be unnecessary for individual subsystems. Also, two novel task-based switching signals are designed to guide the switching among subsystems that do not possess the invariance and attraction of task sets. Furthermore, a common barrier function method, as a special case of the SBF method, is proposed to solve the SCMTC problem for switched systems under arbitrary switchings. Finally, an illustrate example is given to verify the effectiveness of the proposed methods.

The stabilization of the 4D financial system involving the external disturbance and uncertainty is investigated extensively. Firstly, two types of controllers (us) are proposed to stabilize the nominal 4D financial system which is not impacted by the external disturbances. Secondly, three kinds of filters are designed, based on which, three categories of uncertainty and disturbance estimators (uude) are presented and used to asymptotically counteract the lumped disturbance and uncertainty (ud), i.e., buude=−uˆd→−ud, as t→∞, where uˆd is the estimate of ud and b is a known vector. Consequently, the stabilization problem of such a system is implemented by the combined controllers (u=us+uude). It is noted that the obtained controllers are single input controllers, and thus easy to be implemented in applications. Finally, the proposed theoretical results are demonstrated and verified by the computer simulation.

This paper considers continuous transfer function representation for a cascade composed of N mutually interconnected square multiple-input multiple-output (MIMO) linear time-invariant (LTI) subsystems with general multidirectional input–output configurations. Such cascaded structure can arise, e.g., from the spatial discretization of one-dimensional distributed parameter systems (DPSs) described by partial differential equations (PDEs) with boundary conditions representing different configurations of boundary input signals. As shown in the paper, the transfer function matrix of the resulting cascade can be calculated using the Redheffer star product of the subsystems’ transfer function matrices, which simplifies into the usual matrix product for the unidirectional cascade. For the particular case of 2 × 2 cascade composed of rational transfer function subsystems, the recursive formulas for its boundary and distributed transfer functions have been derived for both uni- and multidirectional configurations. The well-posedness and the stability criteria are also analyzed, proving to be more restrictive for the multidirectional cascade than for the unidirectional one due to the internal positive feedback in the first case. As shown in the attached example, the presented results can be used to approximate one-dimensional distributed parameter systems using rational transfer function subsystems representing the spatial sections of the original DPS.

The design of Adaptive Fuzzy Sliding-Mode Control (AFSMC) is discussed in this study for the distributed leader–follower consensus problem of nonlinear uncertain multi-agent systems with input and state constraints. Avoiding the critical circumstances related to the violation of input and state constraints is an important issue in the design of consensus control systems. The limitations of existing adaptive consensus controllers developed for full-state constrained systems motivated the present novel method without restrictive structural assumptions. To convert the original problem to an unconstrained consensus control problem, the proposed control system uses a barrier function-based state transformation method and the input-state linearization methodology. As a result, each agent’s adaptive fuzzy sliding-mode control input, which consists of a fuzzy system and a robust term, is constructed based on the derived representation of the system dynamics. The fuzzy system is used to approximate the dynamic equations of the agent, its neighbors, and maybe the leader in each local feedback control law structure, and the robust term is designed to compensate for the fuzzy approximation error. The magnitudes of the robust terms and the output vectors of the fuzzy systems are also determined using the proposed adaptation laws. The second Lyapunov theorem and Barbalat’s lemma are used to verify the closed-loop system’s asymptotic stability. The effectuality of the proposed methodology is confirmed by numerical simulations for several Autonomous Underwater Vehicles (AUVs). Simulation results show that by means of the proposed AFSMC, the leader–follower consensus is achieved without state constraint violation and performance degradation.

Zeroing neural network (ZNN) has been explored and applied in a variety of time-varying problems solving. However, ZNN models for inequality constrained time-varying linear equation (ICTVLE) solving are rarely reported. Generally, numerous practical problems can be mathematically modeled as ICTVLE problems. Motivated by the above mentioned issue, a nonlinear tunable activation function activated ZNN (NTAF-ZNN) model is constructed to effectively solve ICTVLE problems. To further improve the performances of NTAF-ZNN model, a fuzzy nonlinear tunable activation function (FNTAF) is also designed. Based on the FNTAF, a fuzzy nonlinear tunable activation function-based ZNN (FNTAF-ZNN) model is realized. Firstly, the fixed-time convergence property and disturbance rejection ability of the NTAF-ZNN and FNTAF-ZNN models are proved by theoretical analysis. Then, comparative simulation results of the two models with other existing ZNN models for solving the ICTVLE problem are provided to further verify their robustness and effectiveness. Additionally, the two models and other existing ZNN models are also employed to realize inequality constrained manipulator trajectory tracking under ideal and noisy environments for further comparisons. Finally, the superior performances of the FNTAF-ZNN model for manipulator trajectory tracking are further verified by physical experiment results.

This paper aims to solve the problem of safety-critical control, i.e., safe flight of planar quadcopters in complex environments. By introducing input-to-state safe barrier function (ISSf-BF), the attitude, position, speed, and other key parameters of planar quadcopters are fully considered to realize safety-critical control. Also, a dynamic event-triggered mechanism (DETM) is constructed, and Zeno phenomenon is ruled out based on the constructed DETM. By monitoring the relative distance and speed changes between planar quadcopters and the boundary of the safe zone, the control action is triggered only when the control strategy needs to be adjusted, which effectively reduces the unnecessary waste of computation and communication resources. Finally, a series of simulation experiments are demonstrated to verify the feasibility of the proposed method.

The finite-time distributed state estimation (DSE) problems based on sensor network for discrete-time nonlinear systems are considered in this paper. Considering the uncertainty of the target maneuvers, the interactive multiple models (IMM) based distributed estimation framework is established by local filter and consensus fusion. In the proposed distributed algorithm, partial of the output of the system can be collected by some sensors and the sensor network is supposed to be collectively observable. According to the consensus protocol, the final estimate results are obtained by fusing local estimate results of each sensor after the consensus fusion stage. The distributed estimate results can be obtained with finite-time when the consensus fusion step is larger than the diameter of the network, and the convergence rate of estimate error of the proposed distributed estimate algorithm can be guaranteed. Besides, the existence of the lower and upper bounds of the error covariance matrix are proved with some necessary assumptions. Finally, numerical simulation example is given for tracking the target with different maneuvers.

This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for two distinct scenarios, including convex and strongly convex objectives without the smooth condition. In both scenarios, unlike most of works, an extended version of the conventional path variation is employed to bound the considered performance metric, i.e., dynamic regret. In the convex scenario, a bound O(T1−βDβ(T)+T) is obtained which is comparable to the best-known result, where Dβ(T) is the extended path variation with β∈[0,1) and T being the total number of rounds. In strongly convex case, a bound O(logT(1+T−βDβ(T))) on the dynamic regret is established. In the end, numerical examples are presented to support the theoretical findings.

In this paper, we propose two kinds of prediction–correction methods, discrete-time Euler-smoothing methods, for solving the general time-varying convex constrained optimization problem. By using the complementarity function and smoothing technique, the Karush-Kuhn–Tucker (KKT) trajectory of the problem can be reformulated as a system of smooth equations and considering the dynamics of the system of smooth equations in a discrete constant time-sampling periods scheme. The proposed methods mainly consist of the prediction step derived by Euler approximation and the correction step generated by one or multiple Newton iterations. Under some reasonable conditions, the approximate solution trajectories produced by the methods achieve the asymptotic error bound behaving as O(h4) with respect to optimal trajectory both in the primal and dual space as the smoothing parameter approaches to zero, where h is the sampling period. Finally, the experimental results show that our methods are efficient, and the steady-state tracking errors are much smaller than the other prediction–correction methods under the same conditions.