7 research outputs found
System Level Synthesis via Dynamic Programming
System Level Synthesis (SLS) parametrization facilitates controller synthesis
for large, complex, and distributed systems by incorporating system level
constraints (SLCs) into a convex SLS problem and mapping its solution to stable
controller design. Solving the SLS problem at scale efficiently is challenging,
and current attempts take advantage of special system or controller structures
to speed up the computation in parallel. However, those methods do not
generalize as they rely on the specific system/controller properties.
We argue that it is possible to solve general SLS problems more efficiently
by exploiting the structure of SLS constraints. In particular, we derive
dynamic programming (DP) algorithms to solve SLS problems. In addition to the
plain SLS without any SLCs, we extend DP to tackle infinite horizon SLS
approximation and entrywise linear constraints, which form a superclass of the
locality constraints. Comparing to convex program solver and naive analytical
derivation, DP solves SLS 4 to 12 times faster and scales with little
computation overhead. We also quantize the cost of synthesizing a controller
that stabilizes the system in a finite horizon through simulations
FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking
Real-time, guaranteed safe trajectory planning is vital for navigation in
unknown environments. However, real-time navigation algorithms typically
sacrifice robustness for computation speed. Alternatively, provably safe
trajectory planning tends to be too computationally intensive for real-time
replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that
achieves both real-time replanning and guaranteed safety. In this framework,
real-time computation is achieved by allowing any trajectory planner to use a
simplified \textit{planning model} of the system. The plan is tracked by the
system, represented by a more realistic, higher-dimensional \textit{tracking
model}. We precompute the tracking error bound (TEB) due to mismatch between
the two models and due to external disturbances. We also obtain the
corresponding tracking controller used to stay within the TEB. The
precomputation does not require prior knowledge of the environment. We
demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and
three different real-time trajectory planners with three different
tracking-planning model pairs.Comment: Published in the IEEE Transactions on Automatic Contro
Control and State-Estimation of Jump Stochastic Systems by Learning Recurrent Spatiotemporal Patterns
This thesis establishes control and estimation architectures that combine both model-based and model-free methods by theoretically characterizing several types of jump stochastic systems (JSSs), i.e., systems with random and repetitive jump phenomena. By expanding the capabilities of model-based stochastic control and estimation, there is potential for artificial intelligence to be implemented as a supplement to theory-influenced design instead of being used end-to-end. We begin by deriving sufficient conditions for stochastic incremental stability for nonlinear systems perturbed by two types of non-Gaussian noise: 1) shot noise processes represented as compound Poisson processes, and 2) finite-measure Lévy processes constructed as affine combinations of Gaussian white and Poisson shot noise processes. We then present a controller architecture based on a concept we call pattern-learning for prediction (PLP) for discrete-time/discrete-event systems, in which we can take advantage of the fact that the underlying jump process is a sequence of random variables that occurs as repeated patterns of interest. Finally, we demonstrate control and estimation for JSSs in three real-world applications. First, we consider the control of networks with dynamic topology (e.g., power grid with fault-tolerance to downed lines), for which PLP is integrated with variations of the novel system-level synthesis framework for disturbance-rejection. Second, we perform congestion control of vehicle traffic flow over metropolitan intersection networks, for which PLP is extended to pattern-learning with memory and prediction (PLMP) via the inclusion of episodic control, designed to reduce memory consumption by exploiting structural symmetries and temporal repetition in the network. Third, we perform estimation and forecasting (the dual problem to control) for epidemic spread throughout a population network under jump phenomena such as superspreader effects and the emergence of variant viruses. Our results indicate that learning patterns in the jump process makes controller/observer design efficient in data-consumption and computation time, which suggests that it can potentially be used for other JSSs in the real world