Robust nonblocking supervisory control of discrete-event systems under partial observation

Modern engineering systems and cyber‐physical systems often consist of many distributed and networked physical plants, control units, and other devices with wired or wireless communication networks to exchange information between controllers and plants. These systems are called networked systems. In this article, we review supervisory control of networked discrete‐event systems. We first discuss how to model networked discrete‐event systems and how to obtain state estimates using a networked observer. We then introduce and solve the following supervisory control problems of networked discrete‐event systems: (i) (nondeterministic) supervisory control problem, (ii) deterministic supervisory control problem, (iii) nonblocking supervisory control problem, (iv) robust supervisory control problem, (v) robust deterministic supervisory control problem, (vi) deterministic decentralized supervisory control problem, and (vii) nonblocking decentralized supervisory control problem. We present and prove necessary and sufficient conditions for solving the above problems. Finally, we list the open problems in supervisory control of networked discrete‐event systems.

The signed real measure of regular languages has been introduced and validated in recent literature for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems, where all events are assumed to be observable. This paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level. Thus, for synthesis of DES control systems, the language measure of partially observable discrete-event processes is expressed in a closed form, which is structurally similar to that of completely observable discrete-event processes.

We consider the robust (H???) control problem for linear time-invariant systems over unreliable communication channels that are subject to packet losses from sensors to the controller and from the controller to the actuators. Moreover, the acknowledgments of control packet transmissions are also sent over reverse unreliable communication channels, which is known as the quasi-TCP model. The robust control problem is formulated within a stochastic zero-sum dynamic game framework, from which we obtain an H??? controller that minimizes the worst-case cost function in the presence of an adversary in the dynamical system. We characterize a set of existence conditions of the H??? controller in terms of the disturbance attenuation parameter ?? and packet loss rates. For the least disturbance attenuation scenario (as ?? ??? 8), we show that the H??? control system converges to the corresponding LQG system. We also show that the H??? controller for the TCP- and UDP-cases can be arrived at as appropriate limits of the solution for the quasi-TCP problem. Numerical examples are presented to illustrate the theoretical results.

Maximizing Robustness of Supervisors for Partially Observed Discrete Event Systems

This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty. We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness. Both linear static state feedback and dynamic output feedback controllers are considered. First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established. Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach. As for uncertain systems, we consider structured uncertainty characterized by a dissipative system. This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. LMIbased methods for designing robust dissipative controllers are also derived. The results of this paper unify existing results on H and positive real control and provide a more flexible and less conservative robust control design as it allows for a better trade-off between phase and gain performances.

Existing methods for nonlinear robust control often use scenario‐based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time‐varying uncertainty. This paper draws from local reduction methods used in semi‐infinite optimization to solve robust optimal control problems with parametric and time‐varying uncertainty. By iteratively adding interim worst‐case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst‐case constraint violations. In particular, we present examples where local reduction methods find worst‐case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time‐varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time‐varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

In automated manufacturing systems, resource failures are often inevitable. They reduce the number of available resources and may cause some processing routes of parts to halt and sometimes the whole system to shutdown. This article focuses on the robust deadlock control problem in automated manufacturing systems with multiple resource failures. To obtain such a robust controller, we first put forward a new concept of blocked states of automated manufacturing systems. From such a state, the production of some part types through one of their routes is blocked as caused by resource failures, and only after some failed resources are repaired, these parts can resume their normal processing. Then, these blocked states are characterized in terms of emptied siphons caused by resource failures. In order to prevent the system from deadlocks and blocked states, a robust controller is proposed by the following two steps. First, for siphons without unreliable resources, optimal deadlock control places are added. Then for siphons which contain unreliable resources, new control places are devised to ensure that they could be marked even when resource failures happen. It is proved that the proposed controller can guarantee that all types of parts can be processed repeatedly as long as one unit of unreliable resources can still work. This means that the proposed controller is of greatest robustness, that is, it can tolerate a maximum number of resource failures. Some examples are provided to illustrate the proposed method and show the advantage over the previous ones.

Robust and risk sensitive control of discrete time, finite state systems on an infinite horizon is considered, with either state or output feedback. The solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game. The risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm, and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion. By taking a small noise limit a deterministic dynamic game is obtained, which is closely related to the robust control problem. For the problem with output feedback (partial state information) the analysis depends on introducing appropriate information states for the risk sensitive and robust control problems.

Because of highly complexity and large-scale operation, wastewater treatment process (WWTP) is considered as a robust adaptive control problem. This paper proposes a data-driven robust adaptive control with deep learning (DRAC-DL) for WWTP to improve the operational performance. In ths DRACDL framework, a robust controller is firstly designed to construct the closed-loop control scheme. Meanwhile, an adaptive deep belief network (ADBN) is developed based on the self-incremental learning strategy to approximate the ideal control law. The main advantage of DRAC-DL lies in its improved robustness and low computational burden, which benefit from Lyapunov-based closed-loop controller and efficient ADBN approximator. Finally, the effectiveness of DRAC-DL is demonstrated on the benchmark simulation model No.1 (BSMI) of WWTP.

Decentralized Robust Control of Linear Uncertain Systems

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

Robust velocity and height control problem is dealt with for hypersonic vehicles subject to highly nonlinearity and uncertainties. The linear robust controller design for nonlinear systems suffers from the conservation problem, because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve the dynamic decoupling of the velocity and height channels. Then, robust controllers are designed for each channel to restrain the effects of the parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be counteracted accurately by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system, while the conservation of the robust controller design can be reduced because the nonlinear information of dynamic system is used. Simulation comparisons are given to show the advantages of the proposed robust nonlinear control method.

We develop a process-theoretic approach for generally-dis-tributed discrete-event systems with unrestricted nondeterminism that is geared towards supervisory control. Supervisory control theory deals with synthesis of models of supervisory controllers that ensure safe and nonblocking behavior of the supervised system. The models are synthesized based on a model of the uncontrolled system and a formalization of the control requirements. Even though there exist extensions of supervisory control theory for timed and Markovian discrete-event systems, there are hardly any investigations of supervisory control of discrete-event systems with generally-distributed delays. General distributions provide for (convenient) modeling of important real-world phenomena that cannot be consistently modeled by means of real time or Markovian (exponentially-distributed) delays, like heavy-tail or uniformly distributed processes. Our theory relies on a behavioral preorder termed partial bisimulation, for which we provide a suitable extension. Based on the proposed theory we provide for an appropriate abstraction of the stochastic behavior, which enables us to employ standard supervisory controller synthesis tools. The synthesized supervisor can, thereafter, be coupled with the stochastic model of the unsupervised system and abstracted to a generalized semi-Markov process for the purpose of analysis and simulation.

This paper proposes a unified robust motion controller for the position and force control problems of compliant robot manipulators driven by Series Elastic Actuators (SEAs). It is shown that the dynamic model of the compliant robot includes not only matched but also mismatched disturbances that act on the system through a different channel from the control input. To tackle this complex robust control problem, the unified robust motion controller is synthesised by employing a second-order Disturbance Observer (DOb), which allows us to estimate not only disturbances but also their first and second order derivatives, and a novel controller design approach in state space. By using the Brunovsky canonical form transformation and the estimations of disturbances and their first and second order derivatives, the dynamic model of the robot is reconstructed so that a new system model that includes only matched disturbances is obtained for compliant robots driven by SEAs. The robust position and force controllers are simply designed by eliminating the matched disturbances of the reconstructed system model via the conventional DOb-based robust control method. The stability and performance of the proposed robust motion controllers are verified by simulations.

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming