Research | Daniel E. Ochoa

Hybrid dynamical systems

Hybrid inclusions

\mathcal{H}\;\begin{cases} dx \in F(x)\,dt + \Sigma(x)\,dw_t \qquad &x \in C \\[4pt] x^{+}\in G(x,v_{j+1})\qquad \;\; v \sim \mu \qquad &x \in D \end{cases}

In $C$ the state may flow: it moves continuously, following $F$ , with random noise through $\Sigma$ . In $D$ it may jump: it is reset to a new value, given by $G$ and a random draw $v$ . Where the two sets overlap it may do either, and both $F$ and $G$ can allow several outcomes, so one starting point can have many solutions.

A deterministic example

Robotics A nonholonomic vehicle steers around an obstacle. A hysteretic switch on a logic state picks the side, so adversarial noise at the decision cannot make it chatter.

Algorithm design Momentum dynamics accelerate the descent, and resetting the momentum at the right moments keeps the descent fast and stops it overshooting the minimum.

Networks Systems evolve in continuous time and share information over a communication topology that changes.

Learning A closed loop runs on its current parameter estimate, and the estimate is updated when new data arrives.

Research areas

Learning-enabled control

Guarantees for learned and data-driven hybrid controllers

How can a system learn from data and still be trusted to behave? We study what can be guaranteed about controllers that use learned models or learn while they run.

Topics

Neural hybrid equations
Concurrent learning
Prescribed-time convergence
Approximation guarantees

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