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IDEA Project Summary
This proposal considers networked Cyber-Physical Systems (CPS) in which it is assumed that there is no central
coordinator. Each agent is provided with a local coordinating algorithm that negotiates with its neighbors the value of
the manipulated variables to apply to the plant to ensure stability as well as performance specifications. The objective
of this proposal consists in the development, analysis, and demonstration in case studies of methods to design
controllers for networked CPS based on optimal control (OC).
The project starts by addressing dynamic programming based OC problems to build a single layer integrative control
framework, that is then extended to a distributed optimal and predictive control framework.
The task on dynamic programming based OC problems focus on the study of complex engineering problems
using modern methods of applied mathematics and dynamic optimization. It aims at deriving Hamilton-Jacobi type
conditions, including impulse OC.
The task on algorithms on distributed OC addresses the development of algorithms for these problems by combining
two main steps. In the first, the solution of the necessary conditions of optimality given by the maximum principle are
approximated by a convenient numerical method. In the second, the resulting finite dimensional problem is solved
using the methods of distributed optimization.
The task on distributed model based predictive control (MPC) for network CPS uses system theoretical tools from MPC
for networked CPS. This task is dedicated to research and development of system theoretical tools and algorithms in
the generic framework of distributed Model Predictive Control (MPC) for networked Cyber-Physical Systems (CPS). It
addresses problems in distributed estimation and localization of networked CPS with uncertain relative measures and
communications, distributed MPC for coordinated output regulation in multi-agent systems, and cloud-based MPC
of networked CPS. The control of networked CPS with performance and robustness guarantees poses considerable
theoretical challenges and opportunities since the interactions between the several components of CPS are closed
through limited communication channels, that often present communication jitters, delays, packet dropouts, and noise.
MPC is an optimization-based control strategy that allows optimizing directly over a desired performance index,
representing the desired task, while explicitly imposing system constraints. Moreover, MPC control strategies show
great potential to efficiently and effectively address the design of controllers for CPS because of their ability to produce
predictions of the input and state trajectories which is a significant advantage in networked control when compared with
the classic control strategy where only the control input at the current time step is computed. This feature combined
with event-triggered control strategies with the aim of explicitly take into account the limit resources presented in
many of these embedded systems and physical control architectures, by reducing the number of control actions,
measurements, and communication interactions represent a clear promising direction for the efficient design and
control of networked cyber-physical systems.
Finally, there are two tasks where the concepts developed will be applied, to illustrate them as well as to gain a
source of inspiration for theoretical problems. These applications were chosen to enhance the tight connection of
the project with national and local strategies and include energy management with multiple renewable sources, and
multiple vehicle control and coordination, that considers formation control problems where vehicle replacement needs
to take place.
The main challenges to be addressed by the project are:
Using a measure-driven dynamics framework in relation to the Hamilton-Jacobi-Bellman (HJB) (i) find conditions
under which the solution exists and conditions under which the value function is a solution to the HJB equation,
(ii) obtain relations between the adjoint equation of the Maximum Principle for impulsive control systems and the
solution the associated HJB equations, and appropriate formulation of impulsive feedback control, (iii) obtain HJB type
conditions for systems for sampled impulsive control systems; (iv) to characterize the reachable sets as the level sets
of the value function of optimal control problems using a Hamilton-Jacobi (HJ) approach.
Obtain numerical algorithms for the approximation of distributed optimal control by combining a method to approximate
the conditions of the maximum principle with a method for distributed optimization. Develop methods for distributed
optimization suitable for this propose.
Develop and analyse methods for distributed estimation and localization of networked CPS with uncertain relative
measurements and communications. Develop and analyse in relation to properties of stability and performance
methods for distributed MPC for coordinated output regulation in multi-agent systems. Develop and demonstrate a
methodology for distributed MPC for coordinated output regulation in multi-agent systems. Deve2lop and analyse
coordinated control of multiple agents in multi-layer networked CPS.