Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE–beam systems

This paper addresses the problem of feedback control design for a class of linear cascaded ordinary differential equation (ODE)–partial differential equation (PDE) systems via a boundary interconnection, where the ODE system is linear time-invariant and the PDE system is described by an Euler–Bernoulli beam (EBB) equation with variable coefficients. The objective of this paper is to design a static output feedback (SOF) controller via EBB boundary and ODE measurements such that the resulting closed-loop cascaded system is exponentially stable. The Lyapunov’s direct method is employed to derive the stabilization condition for the cascaded ODE–beam system, which is provided in terms of a set of bilinear matrix inequalities (BMIs). Furthermore, in order to compute the gain matrices of SOF controllers, a two-step procedure is presented to solve the BMI feasibility problem via the existing linear matrix inequality (LMI) optimization techniques. Finally, the numerical simulation is given to illustrate the effectiveness of the proposed design method.     

Chattering free full-order sliding-mode control

In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal sliding-mode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-sliding-mode control scheme. Since the derivatives of terms with fractional powers do not appear in the control law, the control singularities are avoided. A continuous control strategy is developed to achieve the chattering free sliding-mode control. During the ideal sliding-mode motion, the systems behave as a desirable full-order dynamics rather than a desirable reduced-order dynamics. A systematic design method of full-order sliding-mode control for nonlinear systems is presented, which allows both the chattering and singularity problems to be resolved. Simulations validate the proposed chattering free full-order sliding-mode control.     

Event-driven observer-based output feedback control for linear systems

This paper concerns the problem of event-driven observer-based output feedback control of linear systems. Contrary to normal sampled-data control systems, where the controller is updated periodically, in event-driven systems, it is updated only when an “event” happens, and a typical event is defined as some error signals exceeding a given threshold. Both continuous- and discrete-time event detector cases are considered. It is shown that even with the significantly reduced sampling frequency, the global uniform ultimate boundedness of the event-driven closed-loop systems can also be guaranteed. A numerical example is finally used to illustrate the effectiveness and advantages of the proposed approaches.     

Learning control in spatial coordinates for the path-following of autonomous vehicles

We prove the existence of a P-type (proportional-type) space-learning control, which, on the basis of a kinematic third order nonlinear model of an autonomous nonholonomic vehicle and by a proper choice of the proportional control gain, guarantees asymptotic tracking of planar curves whose uncertain curvature is L$L$-periodic in the curvilinear abscissa. The behavior of a human driver, who repetitively learns the correct action from the past experience in the space, is mathematically reproduced. A stability analysis is presented while simulation results demonstrate the effectiveness of the presented approach.     

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of agents described by fully actuated Euler–Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network. In addition, we discuss the case of switching communication topologies in multiagent systems. Finally, we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents.     

Adaptive output-feedback stabilization of non-local hyperbolic PDEs

We address the problem of adaptive output-feedback stabilization of general first-order hyperbolic partial integro-differential equations (PIDE). Such systems are also referred to as PDEs with non-local (in space) terms. We apply control at one boundary, take measurements on the other boundary, and allow the system’s functional coefficients to be unknown. To deal with the absence of both full-state measurement and parameter knowledge, we introduce a pre-transformation (which happens to be based on backstepping) of the system into an observer canonical form. In that form, the problem of adaptive observer design becomes tractable. Both the parameter estimator and the control law employ only the input and output signals (and their histories over one unit of time). Prior to presenting the adaptive design, we present the non-adaptive/baseline controller, which is novel in its own right and facilitates the understanding of the more complex, adaptive system. The parameter estimator is of the gradient type, based on a parametric model in the form of an integral equation relating delayed values of the input and output. For the closed-loop system we establish boundedness of all signals, pointwise in space and time, and convergence of the PDE state to zero pointwise in space. We illustrate our result with a simulation.     

Adaptive model predictive inventory controller for multiproduct warehouse system

An inventory control system has been developed for a distribution system consisting of a single multiproduct warehouse serving a set of customers and purchasing products from multiple vendors. Purchase orders requesting multiple products are delivered to the warehouse in a process referred to as joint replenishment. The receipt of customer orders by the warehouse proceeds in order intervals and in order quantities that are subject to random fluctuations. The objective of warehouse operation is to minimize the total cost while maintaining inventory levels within the warehouse capacity by adjusting the purchase order intervals and quantities. An adaptive model predictive control algorithm is developed using a periodic square wave model to represent the material flows. The adaptive concept incorporates a stabilized minimum variance control-type input calculation coupled with input/output stream parameter predictions. The boundedness of the control output under the suggested algorithm is mathematically proven under the assumption that disturbances in the orders are bounded. The effectiveness of the scheme was demonstrated using simulations.     

A unified method for optimal arbitrary pole placement

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.     

Modularized design for cooperative control and plug-and-play operation of networked heterogeneous systems

In this paper, a cooperative control analysis and design method is investigated for heterogeneous dynamical systems that may be of arbitrary relative degree or nonminimum-phase or both. To achieve consensus or cooperative stability, a negative value of input-feedforward passivity index is used to accommodate and analyze such systems, and the magnitude of the index value is also used as the impact coefficient to quantify the impacts of heterogeneous dynamics of these systems on their networked operations. Physical-system-level designs are explicitly carried out to make individual linear and nonlinear systems (which are either feedback linearizable or nonminimum phase of certain form) become passivity-short and to embed one pure integrator into their input–output dynamics. The network-level distributed control can simply be chosen without any knowledge of the heterogeneous dynamics but with only information of an upper bound on their impact coefficients. It is shown, using the impact equivalence principle, that these controls separately designed but implemented together always ensure either local or global consensus and that a global non-trivial consensus emerges if and only if the information network has at least one globally reachable node or is varying but cumulatively connected. The proposed methodology of fully modularized designs unravels complexity of analyzing and designing cyber–physical systems and enables their plug-and-play into networked operations.     

Output controllability and optimal output control of state-dependent switched Boolean control networks

In the present paper, we investigate the output-controllability and optimal output control problems of a state-dependent switched Boolean control network. By using the semi-tensor product, the algebraic form of the system is obtained. Then, output-controllability problems of the system are discussed and some necessary and sufficient conditions are given. Next, the Mayer-type optimal output control issue is considered and an algorithm is provided to find out the control sequence. At last, an example is given to show the effectiveness of the main results.