| Summary: |
This project aims to:
1. Address the increasingly important class of Hybrid Systems (HS) using Optimal Control (OC) methodologies, in particular the paradigms of multiprocesses and impulsive systems.
2. Continue to develop fundamental tools and results in OC for constrained and nonlinear systems, with specific focus on results with interest to HS.
3. Show the importance and potential benefits of optimal control tools to a wider research community.
Virtually any control problem that is challenging to the research community is nonlinear and has constraints in the inputs and/or states. Many of the complex problems that are the focus of attention of the control community nowadays fall within the so-called Hybrid Systems (HS). Robotic systems are an illustrative example of these two statements: most are nonholonomic and therefore intrinsically nonlinear (cannot be dealt with linear control methods); have constraints on the inputs (limits on the actuators) and on the states (obstacles in the path, safe distances, velocity limits); the description of their evolution is best modeled combining continuous-time dynamical systems (describing physical laws, energy transfers) and discrete-event driven systems (describing the logic of
higher level control layers and mission events).
Optimal control has, for the last 50 years, been developing a body of theory capable of addressing in a systematic and natural way nonlinear systems with input and state constraints. It has also developed tools for some of the most general classes of dynamical systems: governed by differential inclusions, when problem data is not even differentiable or continuous (nonsmooth), with discontinuities in the trajectory (impulsive systems) with several interacting systems (multiprocesses).
It is thus natural that OC is in an excellent position to address in a systematic way the challenges of HS. In our view, the tools of nonsmooth analysis, multiprocesses and impulse control will play an important  |
Summary
This project aims to:
1. Address the increasingly important class of Hybrid Systems (HS) using Optimal Control (OC) methodologies, in particular the paradigms of multiprocesses and impulsive systems.
2. Continue to develop fundamental tools and results in OC for constrained and nonlinear systems, with specific focus on results with interest to HS.
3. Show the importance and potential benefits of optimal control tools to a wider research community.
Virtually any control problem that is challenging to the research community is nonlinear and has constraints in the inputs and/or states. Many of the complex problems that are the focus of attention of the control community nowadays fall within the so-called Hybrid Systems (HS). Robotic systems are an illustrative example of these two statements: most are nonholonomic and therefore intrinsically nonlinear (cannot be dealt with linear control methods); have constraints on the inputs (limits on the actuators) and on the states (obstacles in the path, safe distances, velocity limits); the description of their evolution is best modeled combining continuous-time dynamical systems (describing physical laws, energy transfers) and discrete-event driven systems (describing the logic of
higher level control layers and mission events).
Optimal control has, for the last 50 years, been developing a body of theory capable of addressing in a systematic and natural way nonlinear systems with input and state constraints. It has also developed tools for some of the most general classes of dynamical systems: governed by differential inclusions, when problem data is not even differentiable or continuous (nonsmooth), with discontinuities in the trajectory (impulsive systems) with several interacting systems (multiprocesses).
It is thus natural that OC is in an excellent position to address in a systematic way the challenges of HS. In our view, the tools of nonsmooth analysis, multiprocesses and impulse control will play an important role. Our team gathers worldwide recognized expertise in such tools. Optimal Control research is timely because industry is now open to adopting optimization-based controller design methods. Model predictive control, for example, is an optimization-based control method that has been having a significant and widespread impact in industrial process control, with several thousands of applications reported [M01 and references therein.]. We strongly believe that OC will continue to provide the theoretical foundations for future, much-needed technological developments in many areas of engineering of complex systems. |