Observer Design for (max,+) Linear Systems

This paper deals with control of max-plus linear systems which are discrete event dynamic systems characterized by delays and synchronization phenomena. Control of these discrete event systems consists in choosing the date of input events in order to reach some performances, e.g., to obtain output events at the given dates. This kind of control is optimal according to a just-in-time criterion when the input events dates are delayed as much as possible while ensuring the output events occur before the given output events dates. This paper presents an observed-based controller, where only a subset of the states obtained from measurement is available for the controller. This is an output feedback problem which is solved in two steps, first an observer yields an estimation of the state by using the input and the output measurements, then this estimated state is used in state feedback scheme. The observer and state feedback design is based on the residuation theory which is suitable to deal with mapping inversion defined over order sets

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Supervisory control of discrete-event systems with output : application to hybrid systems

In this thesis, the problem of supervisory control of Discrete-Event Systems (DES) with output is presented and discussed at length. In such systems, causal output functions are employed to assign each sequence of inputs with a corresponding sequence of outputs. When the specification of the desired behavior is given by a formal language over the output alphabet, necessary and sufficient conditions are derived for the existence of nonblocking input as well as nonblocking output supervisory controls. An algorithm is presented to extend the results of nonblocking input/output supervisory control from language-based framework into finite automata framework, making the proposed results applicable to large scale discrete-event systems. The idea of siblings is introduced to solve the problem of nondeterminism in discrete-event abstractions of hybrid systems, giving rise to the development of a theory for nonblocking supervisory control of hybrid systems. Our results enable one to apply classical supervisory control theory to design supervisors for DES approximations of hybrid systems, and to import many interesting concepts from classical theory such as modular and hierarchical control

Event-based H∞ consensus control of multi-agent systems with relative output feedback: The finite-horizon case

In this technical note, the H∞ consensus control problem is investigated over a finite horizon for general discrete time-varying multi-agent systems subject to energy-bounded external disturbances. A decentralized estimation-based output feedback control protocol is put forward via the relative output measurements. A novel event-based mechanism is proposed for each intelligent agent to utilize the available information in order to decide when to broadcast messages and update control input. The aim of the problem addressed is to co-design the time-varying controller and estimator parameters such that the controlled multi-agent systems achieve consensus with a disturbance attenuation level γ over a finite horizon [0,T]. A constrained recursive Riccati difference equation approach is developed to derive the sufficient conditions under which the H∞ consensus performance is guaranteed in the framework of event-based scheme. Furthermore, the desired controller and estimator parameters can be iteratively computed by resorting to the Moore-Penrose pseudo inverse. Finally, the effectiveness of the developed event-based H∞ consensus control strategy is demonstrated in the numerical simulation

Automated model-based testing of hybrid systems

In automated model-based input-output conformance testing, tests are automati- cally generated from a speci¯cation and automatically executed on an implemen- tation. Input is applied to the implementation and output is observed from the implementation. If the observed output is allowed according to the test, then test- ing may continue, or stop with the verdict pass. If the observed output is not allowed according to the test, then testing stops with the verdict fail. The advantages of this test method are that: ² specifications can be reused to test every product in exactly the same way, ² test environments can be controlled because the behavior of the environment is specified as the input of the implementation, ² tests can be generated that a test engineer did not think of yet, ² a huge quantity of tests can be generated and repeated endlessly, and ² the test engineer can focus on testing the parts of the system for which tests are not automated. A hybrid system is a system with both discrete-events and continuous behavior. By continuous behavior we usually mean the behavior of physical quantities over time. A thermostat that observes a chamber temperature and turns on a heater based on the observed temperature change is a system with continuous input and discrete-event output. A robot arm that moves with a certain speed on command (e.g. "GO LEFT") is a system with discrete-event input and continuous output. Within the Tangram project, a four year research project on model-based test and integration methods and their applications, one of the goals was to develop model- based testing for hybrid systems. This involves incorporating continuous behavior and discrete-event behavior into one input-output conformance relation and into a notion of hybrid test. Then, this approach to hybrid model-based testing had to be tried out in practice, in an industrial environment. In this thesis we describe the result of this research. In Chapter 2 and Chapter 3 we define the necessary preliminaries for defining our conformance relation and notion of test for hybrid systems. We use hybrid tran- sition systems to formally represent the implementation and the specification of a system. We base our conformance relation on the discrete-event input-output con- formance relation by Tretmans, and the timed input-output conformance relations by Brandan-Briones and Brinksma, and by Krichen and Tripakis. In Chapter 4 we define our input-output conformance relation for hybrid systems. In this chapter we also define a notion of test for hybrid systems that we have proven sound and exhaustive with respect to the hybrid conformance relation. Based on the notion of hybrid test, we have implemented a proof-of-concept hybrid model-based test tool. The architecture of our tool is based on the TorX test tool and the tests are generated from a hybrid specification using the hybrid  simulation tool. In Chapter 5 we describe TorX and the hybrid X language. In Chapter 6 we describe the issues involved in developing a hybrid model-based test tool in general, and our proof-of-concept tool in particular. In order to better fit theory and practice, we adapt our hybrid input-output conformance relation and notion of test to a conformance relation and notion of test for sampled behavior. We have proven that, under certain conditions, if a hybrid implementation conforms to a hybrid specification, then the implementation also conforms to the specification with sampled behavior. In Chapter 7 we describe the results of a case study that we have performed on a vacuum controller of a waferstepper machine. This controller has sampled con- tinuous input (namely samples of pressure observations) and discrete-event output (namely controlling pumps and valves). We have made a specification that models the sequences of events required for pumping down a vacuum chamber or venting a vacuum chamber. We have modeled the pressure loow in the chamber as continu- ous behavior. With the proof-of-concept tool we have been able to generate tests, stimulate the vacuum control software with sampled pressure low, observe output of the vacuum control software, and give a verdict. We have found a fault in the control software that was not found previously in the field, nor by co-simulation of the controller and a model of the hardware, nor by model checking using Uppaal. This result shows that hybrid model-based testing has added value. In chapter 8 we describe the results of this research and we present some directions for future research

Subpredictor Approach for Event-Triggered Control of Discrete-Time Systems with Input Delays

International audienceWe propose a new output event-triggered control design for linear discrete-time systems with constant arbitrarily long input delays, using delay compensating subpredictors. We prove input-to-state stability of the closed loop system, using framers and the theory of positive systems. A novel feature of our approach is our use of matrices of absolute values, instead of Euclidean norms, in our discrete-time event triggers for our delay compensating control design. We illustrate our approach using a model of the BlueROV2 marine vehicle, where our new event triggers lead to a smaller number of control recomputation times as compared with standard event triggers that were based on Euclidean norms, without sacrificing on settling times or on other performance metrics

Observer-Based Controllers for Max-Plus Linear Systems

Max-plus algebra is a suitable algebraic setting to model discrete event systems involving synchronization and delay phenomena which are often found in transportation networks, communications systems, and manufacturing systems. One way of controlling this kind of systems consists in choosing the dates of input events in order to achieve the desired performances, e.g., to obtain output events in order to respect given dates. This kind of control is optimal, according to a just-in-time criterion, if the input-event dates are delayed as much as possible while ensuring the output events to occur before a desired reference date. This paper presents the observer-based controller for max-plus linear systems where only estimations of system states are available for the controller. As in the classical sense, this is a state-feedback control problem, which is solved in two steps: first, an observer computes an estimation of the state by using the input and the output measurements, then, this estimated state is used to compute the state-feedback control action. As a main result, it is shown that the optimal solution of this observer-based control problem leads to a greater control input than the one obtained with the output feedback strategy. A high throughput screening example in drug discovery illustrates this main result by showing that the scheduling obtained from the observer-based controller is better than the scheduling obtained from the output feedback controller

Model predictive control for discrete event systems with partial synchronization

In this paper, we consider discrete event systems divided in a main system and a secondary system such that the inner dynamics of each system is ruled by standard synchronizations and the interactions between both systems are expressed by partial synchronizations (i.e., event e2 can only occur when, not after, event e1 occurs) of events in the secondary system by events in the main system. The main contribution consists in adapting model predictive control, developed in the literature for (max,+)-linear systems, to the considered class of systems. This problem is solved under the condition that the performance of the main system is never degraded to improve the performance of the secondary system. Then, the optimal input is selected to respect the output reference and the remaining degrees of freedom are used to ensure just-in-time behavior. The unconstrained problem is solved in linear time with respect to the length of the prediction horizon