*Pierre-Loïc Garoche*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter summarizes an attempt to express classical notions of control theory such as stability or robustness using the previously presented invariant-based tools. All numerical tools presented ...
More

This chapter summarizes an attempt to express classical notions of control theory such as stability or robustness using the previously presented invariant-based tools. All numerical tools presented in previous chapters were focused on the precise over-approximation of reachable states. However, this chapter argues that it is important to be able to express higher level properties than just bounding reachable states. The idea that drove the invariants and template synthesis after all was this notion of Lyapunov functions and of Lyapunov stability. Assuming a control level property, it would be extremely interesting to be able to express this property over the code or model artifact. A main limitation for the study of these control level properties is the need for the plant description, which is generally not available when considering code artifact. As such, this chapter assumes the plant semantics is provided in a discrete fashion and therefore amenable to code level description as presented in Chapter 3.Less

This chapter summarizes an attempt to express classical notions of control theory such as stability or robustness using the previously presented invariant-based tools. All numerical tools presented in previous chapters were focused on the precise over-approximation of reachable states. However, this chapter argues that it is important to be able to express higher level properties than just bounding reachable states. The idea that drove the invariants and template synthesis after all was this notion of Lyapunov functions and of Lyapunov stability. Assuming a control level property, it would be extremely interesting to be able to express this property over the code or model artifact. A main limitation for the study of these control level properties is the need for the plant description, which is generally not available when considering code artifact. As such, this chapter assumes the plant semantics is provided in a discrete fashion and therefore amenable to code level description as presented in Chapter 3.

*Pierre-Loïc Garoche*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a ...
More

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a typical object used in control systems or in signal processing. In some cases, it is eventually implemented in a program to perform the desired feedback control to a cyber-physical system. Language-wise, model-based languages such as LUSTRE, ANSYS SCADE, or MATLAB Simulink provide primitives to build these dynamical systems or controllers relying on simpler constructs. In terms of programs, such dynamical systems can easily be implemented as a “while true loop” initialized by the initial state and performing the update f. The simplest systems are usually directly coded in the target language, while more advanced systems are compiled through autocoders.Less

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a typical object used in control systems or in signal processing. In some cases, it is eventually implemented in a program to perform the desired feedback control to a cyber-physical system. Language-wise, model-based languages such as LUSTRE, ANSYS SCADE, or MATLAB Simulink provide primitives to build these dynamical systems or controllers relying on simpler constructs. In terms of programs, such dynamical systems can easily be implemented as a “while true loop” initialized by the initial state and performing the update *f*. The simplest systems are usually directly coded in the target language, while more advanced systems are compiled through autocoders.