Tao Zou

A finite-time approach to formation control of multiple mobile robots with terminal sliding mode

In this study, a new finite-time synchronised approach is developed for multiple mobile robots formation control based on terminal sliding mode control principle and system synchronisation theory. Associated stability analysis is presented to lay a foundation for analytical understanding in generic theoretical aspects and safe operation for real systems. An illustrative example of multiple mobile robots formation control is bench tested to validate the effectiveness of the proposed approach.

Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi–Sugeno's form

Abstract This paper studies stabilization of the Takagi–Sugeno fuzzy system with input and state constraints and bounded noise. The technique of extended nonquadratic boundedness is proposed based on the existing quadratic boundedness. Under the non-parallel distributed compensation law, the state of the closed-loop system is stabilizing to a neighborhood of the origin specified via an extended nonquadratic Lyapunov function. The existing technique for relaxing the linear matrix inequality conditions can be properly applied to obtain computationally tractable stability conditions. A simulation example is given to show the effectiveness of the controller.

Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials

Abstract The stability and stabilization conditions of the nonlinear system in Takagi–Sugenos form are considered. The homogeneously polynomially nonquadratic (HPNQ) Lyapunov functions and homogeneously polynomially parameterized (HPP) state feedback laws are adopted. By generalizing the procedure based on the Polyas theorem, the asymptotically necessary and sufficient (ANS) stability and stabilization conditions in the case of HPNQ Lyapunov functions and HPP control laws are reformulated. The major contribution of this paper is to give the parallel results using the multiple indices, so that the slack matrices can be extensively utilized to improve the numerical efficiency. The effectiveness of the results is illustrated by the numerical examples.

Compatibility and Uniqueness Analyses of Steady State Solution for Multi-variable Predictive Control Systems

The multi-variable control systems can be structurally classified into the square and non-square ones,with the latter further into fat and thin ones.For the fat and thin,the output offset and non-determinedness of the steady state input,respectively,can occur in predictive control systems.From the steady-state relationship between the control input and the controlled output,the two issues are tackled as the compatibility and uniqueness,respectively,of the nonhomogeneous linear equations set.The reason why the compatibility and uniqueness issues can arise is analyzed based on the determination theorem for non-homogeneous linear equations set,and the solutions based on the double-layer(two-layer) control structure are given.The upper level steady state optimization not only tackles the compatibility issue for the thin system,but also finds the optimal solution from the infinite many consistent ones for the fat system.The lower level predictive control algorithm,integrated with the control input target,guarantees the uniqueness of the steady state solution for fat system,and algorithmically unifies both the square and nonsquare systems.Simulation results have validated the effectiveness of the double-layered predictive control algorithm,i.e.,the steady state solutions of the multi-variable predictive control system are consistent and unique.

Offset-Free Strategy by Double-Layered Linear Model Predictive Control

In the real applications, the model predictive control (MPC) technology is separated into two layers, that is, a layer of conventional dynamic controller, based on which is an added layer of steady-state target calculation. In the literature, conditions for offset-free linear model predictive control are given for combined estimator (for both the artificial disturbance and system state), steady-state target calculation, and dynamic controller. Usually, the offset-free property of the double-layered MPC is obtained under the assumption that the system is asymptotically stable. This paper considers the dynamic stability property of the double-layered MPC.

Dynamic output feedback robust MPC with relaxed constraint handling for LPV system with bounded disturbance

For the constrained linear parameter varying (LPV) system with bounded disturbance, a dynamic output feedback model predictive control (MPC), with a series of scalars for relaxing the disturbance-related constraints handling, is proposed. An optimization procedure, for off-line determining the relaxation scalars, is proposed based on the norm-bounding technique. The augmented state of the closed-loop system is guaranteed to converge to the neighborhood the equilibrium point. A numerical example is given to show the effectiveness of the results.

A steady-state target calculation method based on “point” model for integrating processes

Aiming to eliminate the influences of model uncertainty on the steady-state target calculation for integrating processes, this paper presented an optimization method based on point model and a method determining whether or not there is a feasible solution of steady-state target. The optimization method resolves the steady-state optimization problem of integrating processes under the framework of two-stage structure, which builds a simple point model for the steady-state prediction, and compensates the error between point model and real process in each sampling interval. Simulation results illustrate that the outputs of integrating variables can be restricted within the constraints, and the calculation errors between actual outputs and optimal set-points are small, which indicate that the steady-state prediction model can predict the future outputs of integrating variables accurately.

On MPC of linear system over networks with bounded delays and packet losses

This paper studies the model predictive control (MPC) of the networked control systems (NCSs) where arbitrary bounded deterministic network-induced delays and packet losses may occur in both sensor to controller and controller to actuator links. A new augmented model, which is specially suitable to the on-line refreshed control law, is proposed, based on which an approach of networked MPC is proposed by extending the previous one for NCS with only packet losses. It is shown that closed-loop stability is guaranteed by the proposed approach, satisfying the input and state constraints. A numerical example is given to illustrate the effectiveness of the proposed MPC.

An approach of constraint boundaries tuning based on shadow price for two-layered predictive control

Shadow prices show the effect, which were caused by variations of constrained boundaries, to optimum value of objective function under the current optimal strategy. In this paper, a LP-MPC form of two-layered predictive control was described, and a constraint tuning strategy based on shadow price was proposed under this structure. The nature of disturbance can be evaluated according to the history data of process, then, combine with constraint conditions of the process, tuning boundaries will be obtained. The shadow prices for constrained boundaries of steady-state target calculation were counted based on solving a linear programming and its dual problem. Then, the constraint boundaries, which influence the objective optimum effectively, were handled selectively. The process will be pushed to allowable operation boundaries, to increase the economic benefit. Finally, in a practical process, a simulation example was conducted in order to verify the useful of shadow price to constraint tuning for two-layered predictive control.

Geometric characterization of multi-input lower-triangular forms

This paper is concerned with the problem as to whether a multi-input nonlinear system is equivalent to the so-called low-triangular form. Two elemental forms of multi-input lower-triangular systems are proposed. Then, using the theory of singular distributions, the necessary and sufficient conditions under which multi-input nonlinear systems are locally feedback equivalent to these two lower-triangular systems are established. Furthermore, algorithms are provided to describe how to realize these equivalent transformations via state feedbacks and coordinate conversions.