Automation department seminar "Optimal multi-objective time-energy control".

Optimal time-dependent control often uses a transformation of the value function, known as the Kruzkov transformation.

Although primarily used for time-optimal problems, this transformation can be applied to broader cost functions, offering significant advantages in dynamic programming approaches based on policy iteration, notably by eliminating the need for an initial admissible policy.

Despite its advantages, the Kruzkov transformation converges exponentially fast to one, which can lead to numerical instabilities when the original value function takes on large values.

To remedy this, we propose a new transformation, called the harmonic transformation, which alleviates these numerical problems at the cost of introducing additional nonlinearities into the problem.

With this new transformation, we analyze how the dynamic programming principle adapts and introduce a semi-Lagrangian numerical scheme with proven convergence guarantees, adopting a value iteration framework.

Focusing on time- and energy-optimal control problems, we extend the formulation to a multi-objective context, aiming to approximate the Pareto set of efficient solutions.

Two solution approaches, based on policy iteration, are proposed: one deterministic and one evolutionary.

The presentation includes several examples that illustrate the performance of both methods, including scenarios with obstacles, forbidden regions and time-varying dynamics.

Víctor Campos has been a professor in the Department of Electronic Engineering at the Universidade Federal de Minas Gerais (UFMG) since 2018.

He is a member of the Intelligent Transportation Group (ITG) and coordinator of the undergraduate program in Control and Automation Engineering.

He received his bachelor's, master's and doctoral degrees from UFMG in 2009, 2010 and 2015, respectively, and completed a doctoral internship at LAMIH (France) and UCSB (USA) in 2014.

His research focuses on Takagi-Sugeno fuzzy systems, optimization-based control synthesis, robust and adaptive control, and motion planning.