Unbounded Disturbances Research Articles

Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

This paper proposes a distributed consensus algorithm in predefined time of time‐varying optimization with inequality constrains for multi‐agent systems (MASs) with external disturbances over an undirected graph. Firstly, by utilizing exponential function, a novel criterion with respect to the stability in predefined time is developed for the nonlinear systems. Secondly, a new distributed switching control protocol, which can inhibit the external unbounded disturbances, is piecewise designed to drive the states of agents to the sliding mode surface via the predefined‐time set by users. Subsequently, under the designed event‐triggered controller (ETC), the states of agents achieve consensus in predefined time on the sliding mode surface. Meanwhile, with the help of log barrier function, the consensus states of agents reach the feasible region and converge to the optimal solution in predefined time. Finally, the correctness and availability of the proposed optimization control algorithm are verified by a simulation example.

SEMG data driven-based anti-disturbance control enables adaptive interaction of lower limb rehabilitation exoskeleton

The efficient human–machine interaction control is the core of human–machine integration, which can improve the tracking accuracy of the lower limb rehabilitation exoskeleton system and the compliance of human–machine cooperative movement. However, the non-ideal factors such as mechanical friction, model uncertainties, iteration errors and external interference in the training process undoubtedly bring potential dangers to the safety of rehabilitation training. Consequently, to escape unnecessary damage caused by external disturbances (especially the unbounded disturbances) during rehabilitation training, a noise-suppressing zeroing neural network human–machine interaction controller is developed in this work, which is based on the constructed human–machine coupling dynamic model and the active motion intention (active torque) of the subject identified by exploiting the deep convolutional neural network. The simulation experiments and statistical analyses verify that the present noise-suppressing zeroing neural network controller can be applied to monitor the lower limb rehabilitation exoskeleton for assisting the subjects in various task with the external disturbances,and the average root mean square error of the hip, knee and ankle joints’ angles are 0.0015rad, 0.0051rad and 0.0056rad, respectively. Furthermore, a novel model predictive control is developed and analyzed based on noise-suppressing zeroing neural network controller, which can effectively constrain the angle and angular velocity of the lower limb rehabilitation exoskeleton. The root mean square errors of hip, knee and ankle joint angle are 0.0032rad, 0.0078rad, and 0.0085rad, respectively. Finally, the platform experiment verifies that the proposed controllers can be utilized to control the lower limb rehabilitation exoskeleton to assist the subjects in rehabilitation training.

Robust Learning-Based Model Predictive Control for Intelligent Vehicles With Unknown Dynamics and Unbounded Disturbances

Robust Learning-Based Model Predictive Control for Intelligent Vehicles With Unknown Dynamics and Unbounded Disturbances

Separation and Rendezvous Control of the UAV-USV Subsystem based on Distributed SMPC with Unbounded Disturbances

Separation and Rendezvous Control of the UAV-USV Subsystem based on Distributed SMPC with Unbounded Disturbances

Constrained Receding Horizon Output Estimation of Linear Distributed Parameter Systems

We address constrained output estimation of discrete-time linear distributed parameter systems in the presence of plant and measurement disturbances. Sufficient conditions are proposed for the strong stability of the proposed moving horizon estimator. We further show that the discrete-time estimation results can be linked to continuous-time infinite-dimensional systems described by partial differential equations (PDEs) with unbounded disturbance and output operators by using Cayley-Tustin transformation. The theoretical results are illustrated with numerical examples on a one-dimensional (1D) wave equation and a 1D diffusion.

On stabilization of an axially moving string with a tip mass subject to an unbounded disturbance

This paper deals with the stabilization problem of an axially moving string with a tip mass attached at the free end and subject to an external disturbance. The disturbance here is not uniformly bounded, and it is assumed to be exponentially increasing. First, the tip mass equation is designed under a boundary controller. By using this equation, the active disturbance rejection control (ADRC) technique is applied to design a disturbance observer, and it is shown that the observer can be estimated exponentially. Then, the closed‐loop system is formulated and the well‐posedness of the model is proved in the framework of the semigroup theory. The stability of the closed‐loop system is then proved by means of the multiplier technique, where the energy system converges to equilibrium with an exponential manner. The efficiency of the obtained results is verified through numerical simulations.

Stabilization of Nonlinear Systems with External Disturbances Using the DE-Based Control Method

This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results.

Fuzzy optimized conditioned-barrier nonlinear control of electric vehicle for grid to vehicle & vehicle to grid applications

Plug-in electric vehicle (PEV) is the long-term eco-friendly solution to conventional fossil fuel based vehicles. In this study, a novel nonlinear barrier conditioned super-twisting sliding mode controller (BC ST-SMC) is proposed for the control of the PEV. The conventional super-twisting sliding mode control (ST-SMC) can only cater for the disturbances with known bounds and exhibits wind-up effects in the presence of saturated inputs which deteriorates the closed-loop performance of the system. The proposed BC-ST SMC solves these problems by providing anti-windup and un-bounded disturbance rejection. Lyapunov stability criterion is used to prove the asymptotic stability of the system. The PEV comprises of two subsystems namely: bidirectional charging unit (BCU) and hybrid energy storage system (HESS). The BCU comprises of a totem pole power converter between the PEV and grid which operates in two modes of grid to vehicle (G2V) and vehicle to grid (V2G). The components of the HESS are the battery and regenerative fuel-cell (RFC) (i.e. fuel-cell (FC) with an electrolyzer). The electrolyzer generates hydrogen which is required for the FC. Fuzzy-logic based energy management system (EMS) is adopted to maintain the power balance using state of charge (SoC) of the battery and electrolyzer as inputs. Furthermore, the controller gains are tuned using multi-objective genetic algorithm (MOGA) and multi-objective grey wolf optimizer (MOGWO) using integral absolute derivative of control input (IADU) with integral square of the error (ISE) as a fitness function. The simulations are performed on MATLAB® Simulink (2022b) which proves the superior performance of BC ST-SMC over conventional nonlinear controllers in the presence of saturated inputs. Finally, hardware-in-loop (HIL) based experimental results verify the real-time control of the proposed PEV.

Stabilization of Linear Time-Invariant Systems With Unbounded Disturbances via DE-Based Control Method

Stabilization of Linear Time-Invariant Systems With Unbounded Disturbances via DE-Based Control Method

Generalized zeroing neural dynamics model for online solving time-varying cube roots problem with various external disturbances in different domains

As a basic problem of the nonlinear dynamic model, the online solution of time-varying cube root problem (TVCRP) is widely used in science and engineering. However, the practical system is frequently disturbed by the external factors, which inevitably leads to unknown disturbances in the solution process. Therefore, addressing the TVCRP with high accuracy in non-ideal environment (unknown disturbances) is the basis of solving the nonlinear dynamic model. In this work, a noise-suppression zeroing neural dynamics (NSZND) model is investigated and developed from the control perspective to resolve the time-varying or time-invariant cube root problem with the different disturbances (bounded and unbounded disturbances) in real/complex domain. Moreover, the generalized noise-suppression zeroing neural dynamics model with various activation functions is discussed and designed for eliminating the interference of different disturbances to improve the precision and noise immunity of the NSZND model. The global/exponential convergence of the developed models with various disturbances are proved by theoretical analyses. With unbounded disturbance (linear noise), the solving accuracy of the NSZND model is about 101 and 103 times superior to the gradient neural dynamics model and the zeroing neural dynamics model. Finally, the proposed NSZND model is extended to the tensor cube root problem, and the feasibility of the proposed model is verified in this work. Beyong that, different fractals are generated by using the proposed model to solve the cube root problem in the complex domain, which provides an interesting idea for advertising design and computer graphics.

A noise-suppressing neural network approach for upper limb human-machine interactive control based on sEMG signals.

The use of upper limb rehabilitation robots to assist the affected limbs for active rehabilitation training is an inevitable trend in the field of rehabilitation medicine. In particular, the active motion intention-based control of the upper limb rehabilitation robots to assist subjects in rehabilitation training is a hot research topic in human-computer interaction control. Therefore, improving the accuracy of active motion intention recognition is the premise of the human-machine interaction controller design. Furthermore, there are external disturbances (bounded/unbounded disturbances) during rehabilitation training, which seriously threaten the safety of subjects. Thereby, eliminating external disturbances (especially unbounded disturbances) is the difficulty and key to the human-machine interaction control of the upper limb rehabilitation robots. In response to these problems, based on the surface electromyogram signal of the human upper limb, this paper proposes a fuzzy neural network active motion intention recognition method to explore the internal connection between the surface electromyogram signal of the human upper limb and active motion intention, and improve the real-time and accuracy of recognition. Based on this, two types of human-machine interaction controllers, which can be called as zeroing neural network controller and noise-suppressing zeroing neural network controller are designed to establish a safe and comfortable training environment to avoid secondary damage to the affected limb. Numerical experiments verify the feasibility and effectiveness of the proposed theories and methods.

Stochastic Model Predictive Control using Initial State Optimization

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the MPC. The scheme avoids the infeasibility issues arising from unbounded disturbances by including the initial state as a decision variable. We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances. In addition to illustrating these guarantees, the numerical example indicates further advantages of optimizing over the initial state for the transient behavior.

Recursively Feasible Stochastic Predictive Control Using an Interpolating Initial State Constraint

We present a stochastic model predictive control (SMPC) framework for linear systems subject to possibly unbounded disturbances. State of the art SMPC approaches with closed-loop chance constraint satisfaction recursively initialize the nominal state based on the previously predicted nominal state or possibly the measured state under some case distinction. We improve these initialization strategies by allowing for a continuous optimization over the nominal initial state in an interpolation of these two extremes. The resulting SMPC scheme can be implemented as one standard quadratic program and is more flexible compared to state-of-the-art initialization strategies. As the main technical contribution, we show that the proposed SMPC framework also ensures closed-loop satisfaction of chance constraints and suitable performance bounds.

Stochastic model predictive control for spacecraft rendezvous and docking via a distributionally robust optimization approach

A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance. doi:10.1017/S1446181121000031

Lagrangian approximations for stochastic reachability of a target tube

We consider the problem of stochastic reachability of a target tube for a discrete-time, stochastic dynamical system with bounded control authority. We propose grid-free algorithms to compute under- and over-approximations of the stochastic reach set, and a corresponding feedback-based controller associated with a given likelihood. Our approach employs set-theoretic (Lagrangian) techniques for nonlinear systems with affine stochastic disturbances. With available set computation tools, these algorithms can only be implemented on linear systems. We use the law of total probability to partition the potentially unbounded disturbance set, and compute minimal and maximal reach sets via a robust approach. We propose a heuristic to partition the disturbance set using an ellipsoid when the disturbance is Gaussian, and a polyhedron otherwise. For linear dynamics and convex and compact sets, we employ existing tools from support functions and robust linear programming to efficiently approximate the stochastic reach set. We synthesize an admissible controller using the disturbance minimal reach sets by solving a series of linear programs. We demonstrate our approach on systems with linear dynamics (time-invariant and time-varying) and arbitrary disturbances (as well as Gaussian), including trajectory following for a Dubin’s vehicle and space vehicle rendezvous and docking.

Experimental study of event-based neural network control on parallel manipulator

In the paper, the event-based switching controller (ESC) is utilized to achieve better tracking performance compared with the neural network controller in circumstance of parameter uncertainty and unknown disturbance for the parallel manipulator. The ESC optimizes the choice of the neural weights by combining the prior knowledge of the system dynamics and the estimation of the system parameters. To implement the controller, a general method of computing the system regression matrix for the PM is proposed and the stability proof is given in circumstance of unbounded disturbance. The ESC is tested by the simulated Delta manipulator and the experimental 5R testbed. The results show the effectiveness of the proposed controller.

STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

AbstractA stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

Probabilistic Model Predictive Safety Certification for Learning-Based Control

Reinforcement learning (RL) methods have demonstrated their efficiency in simulation. However, many of the applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified closed-loop behavior in order to meet the safety specifications in the presence of physical constraints. This article introduces a concept called probabilistic model predictive safety certification (PMPSC), which can be combined with any RL algorithm and provides provable safety certificates in terms of state and input chance constraints for potentially large-scale systems. The certificate is realized through a stochastic tube that safely connects the current system state with a terminal set of states that is known to be safe. A novel formulation allows a recursively feasible real-time computation of such probabilistic tubes, despite the presence of possibly unbounded disturbances. A design procedure for PMPSC relying on Bayesian inference and recent advances in probabilistic set invariance is presented. Using a numerical car simulation, the method and its design procedure are illustrated by enhancing an RL algorithm with safety certificates.

Recursively feasible stochastic model predictive control using indirect feedback

We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening. We introduce an initialization of each MPC iteration which is always recursively feasible and guarantees chance constraint satisfaction for the closed-loop system, which is typically challenging for systems under unbounded disturbances. Under an i.i.d. zero-mean assumption, we provide an average asymptotic performance bound. A building control example illustrates the approach in an application with time-varying, correlated disturbances.

Measurement Maximizing Adaptive Sampling with Risk Bounding Functions

In autonomous exploration a mobile agent must adapt to new measurements to seek high reward, but disturbances cause a probability of collision that must be traded off against expected reward. This paper considers an autonomous agent tasked with maximizing measurements from a Gaussian Process while subject to unbounded disturbances. We seek an adaptive policy in which the maximum allowed probability of failure is constrained as a function of the expected reward. The policy is found using an extension to Monte Carlo Tree Search (MCTS) which bounds probability of failure. We apply MCTS to a sequence of approximating problems, which allows constraint satisfying actions to be found in an anytime manner. Our innovation lies in defining the approximating problems and replanning strategy such that the probability of failure constraint is guaranteed to be satisfied over the true policy. The approach does not need to plan for all measurements explicitly or constrain planning based only on the measurements that were observed. To the best of our knowledge, our approach is the first to enforce probability of failure constraints in adaptive sampling. Through experiments on real bathymetric data and simulated measurements, we show our algorithm allows an agent to take dangerous actions only when the reward justifies the risk. We then verify through Monte Carlo simulations that failure bounds are satisfied.