A Control-Oriented Notion of Finite State Approximation

We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust control, we propose a control-oriented notion of finite state approximation for these systems, demonstrate its relevance to the control synthesis problem, and discuss its key features.Comment: IEEE Transactions on Automatic Control, to appea

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples

Solving Commutative Relaxations of Word Problems

We present an algebraic characterization of the standard commutative relaxation of the word problem in terms of a polynomial equality. We then consider a variant of the commutative word problem, referred to as the “Zero-to-All reachability” problem. We show that this problem is equivalent to a finite number of commutative word problems, and we use this insight to derive necessary conditions for Zero-to-All reachability. We conclude with a set of illustrative examples

A finite state machine framework for robust analysis and control of hybrid systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 107-115).Hybrid systems, describing interactions between analog and discrete dynamics, are pervasive in engineered systems and pose unique, challenging performance verification and control synthesis problems. Existing approaches either lead to computationally intensive and sometimes undecidable problems, or make use of highly specialized discrete abstractions with questionable robustness properties. The thesis addresses some of these challenges by developing a systematic, computationally tractable approach for design and certification of systems with discrete, finite-valued actuation and sensing. This approach is inspired by classical robust control, and is based on the use of finite state machines as nominal models of the hybrid systems. The development does not assume a particular algebraic or topological structure on the signal sets. The thesis adopts an input/output view of systems, proposes specific classes of inequality constraints to describe performance objectives, and presents corresponding 'small gain' type arguments for robust performance verification. A notion of approximation that is compatible with the goal of controller synthesis is defined. An approximation architecture that is capable of handling unstable systems is also proposed.(cont.) Constructive algorithms for generating finite state machine approximations of the hybrid systems of interest, and for efficiently computing a-posteriori bounds on the approximation error are presented. Analysis of finite state machine models, which reduces to searching for an appropriate storage function, is also shown to be related to the problem of checking for the existence of negative cost cycles in a network, thus allowing for a verification algorithm with polynomial worst-case complexity. Synthesis of robust control laws is shown to reduce to solving a discrete, infinite horizon min-max problem. The resulting controllers consist of a finite state machine state observer for the hybrid system and a memoryless full state feedback switching control law. The use of this framework is demonstrated through a simple benchmark example, the problem of stabilizing a double integrator using switched gain feedback and binary sensing. Finally, some extensions to incremental performance objectives and robustness measures are presented.by Danielle C. Tarraf.Ph.D

Unloader for rotary compressors

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (p. 139).The capacity of rolling piston type rotary compressors is typically varied by using variable speed motor drives. That entails the use of high cost electronics. This study explores an alternative means of achieving variable capacity while keeping motor speed constant, by lifting the vane intermittently. The new technique should deliver comparable system performance and efficiency at lower initial costs in order to be competitive. The thesis starts by analyzing the kinematics and dynamics of the vane motion using simplified working models of the system. Also, the interaction between the vane and the rolling piston is modeled, with focus on possible impact between the moving parts. Next, the functional requirements for a vane lifting mechanism are set. The details of the design are worked out, and a complete set of engineering drawings is fully developed. A prototype of the mechanism was constructed; a brief description of the process is given. The last part of the thesis presents the experimental work done to prove the success of the concept, to assess the mechanism, and to determine optimal operation modes. The prototype is shown to fulfill its goal of varying system capacity. The weaknesses of the design are pointed out. Some effort is made to single out the parameters that set optimal cycling times. The main findings of the experiments are presented in a brief conclusion. Recommendations are made for second generation mechanism designs and for developing criteria for cycle time optimization.by Danielle C. Tarraf.S.M

On the nature and stability of differential-algebraic systems

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