Verification and Control of Hybrid Systems: A Symbolic by Paulo Tabuada

By Paulo Tabuada

Hybrid structures describe the interplay of software program, modeled by way of finite-state structures reminiscent of finite-state machines, with the actual international, defined via infinite-state structures reminiscent of differential equations. Verification and keep an eye on of Hybrid Systems presents a special systematic exposition of a number of periods of hybrid platforms, admitting symbolic versions in addition to the relationships among them. The textual content outlines a number of key verification and keep an eye on synthesis effects for hybrid structures, guided by means of the concept that of bisimulation, and illustrated by way of a number of examples.

The e-book is split into 4 parts:

Part I offers easy options founded on a idea of approach that's basic sufficient to explain finite-state, infinite-state, and hybrid systems.

Part II discusses the ways that structures relate to different structures, akin to behavioral inclusion/equivalence and simulation/bisimulation, utilizing those relationships to review verification and keep watch over synthesis difficulties for finite-state systems.

Part III attracts concept from timed automata to give numerous sessions of hybrid platforms, with richer non-stop dynamics, that may be regarding finite-state symbolic structures. as soon as such relationships are tested, verification and keep an eye on synthesis difficulties for those hybrid platforms could be instantly solved through resorting to the options defined partially II for finite-state platforms.

Part IV follows an identical method by way of generalizing simulation/bisimulation relationships to approximate simulation/bisimulation relationships that may be used for a much wider classification of hybrid systems.

This finished therapy will attract researchers, engineers, desktop scientists, and graduate scholars within the components of formal equipment, verification, version checking, and regulate and may certainly encourage extra learn of the really expert literature.

Show description

Read or Download Verification and Control of Hybrid Systems: A Symbolic Approach PDF

Similar control systems books

Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach

Strength alternate is an immense beginning of the dynamics of actual platforms, and, for this reason, within the research of complicated multi-domain platforms, methodologies that explicitly describe the topology of strength exchanges are instrumental in structuring the modeling and the computation of the system's dynamics and its regulate.

Intelligent Diagnosis and Prognosis of Industrial Networked Systems (Automation and Control Engineering)

In an period of extensive pageant the place plant working efficiencies needs to be maximized, downtime as a result of equipment failure has turn into extra high priced. to chop working expenditures and raise sales, industries have an pressing have to expect fault development and ultimate lifespan of commercial machines, techniques, and structures.

Fault Detection and Diagnosis in Engineering Systems

That includes a model-based method of fault detection and analysis in engineering structures, this booklet includes updated, sensible details on combating product deterioration, functionality degradation and significant equipment harm. ;College or college bookstores could order 5 or extra copies at a different scholar rate.

Extra info for Verification and Control of Hybrid Systems: A Symbolic Approach

Example text

1) System Sb is typically a model of the specification that is to be enforced, on a given platform modeled by Sa , through the design of Sc . The control problem for equivalence makes sense at different levels of design. System Sa could model a hardware platform and Sc could model an operating system to be designed or Sa could model the hardware platform equipped with the operating system and Sc could be the desired midleware or application level software. 1), formal verification is not necessary to prove the equivalence between the designed system Sc ×I Sa and the specification Sb .

7. 19). Such hybrid model can be ✲ ) with: described by the system S = (X, U, • X = {s1 , s2 } × R2 ; • U = {u1 , u2 } ∪ R+ 0; u ✲ • (s, iL , vC ) (s , iL , vC ) if one of the following four conditions holds: 1. u = u1 , s = s1 , iL = iL , and vC = vC ; 2. u = u2 , s = s2 , iL = iL , and vC = vC ; 2 3. 17) satisfying ξ(0) = (iL , vC ) and ξ(u) = (iL , vC ); 2 4. 19) satisfying ξ(0) = (iL , vC ) and ξ(u) = (iL , vC ). For this hybrid system the invariants are Ins1 = R2 = Ins2 , the guards are Gu(s1 ,u,s2 ) = R2 = Gu(s2 ,u,s1 ) , and the reset maps are Re(s1 ,u,s2 ) = 1R2 = Re(s2 ,u,s1 ) for any u ∈ {u1 , u2 }.

In our game theoretic interpretation, we can play one game to show that Sa B Sb and another game to show that Sb B Sa . If the first game is won by Sb , and the second game is won by Sa , then the systems are behaviorally equivalent. Alternatively, we can combine the two games into a single game, where in each round of the combined game we arbitrarily choose which system plays first, and which systems plays second. If, in every round, the system that plays second can always match the system that plays first, regardless of the choice, then the systems are behaviorally equivalent.

Download PDF sample

Rated 4.12 of 5 – based on 50 votes