17 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
System level parameterizations, constraints and synthesis
We introduce the system level approach to controller synthesis, which is composed of three elements: System Level Parameterizations (SLPs), System Level Constraints (SLCs) and System Level Synthesis (SLS) problems. SLPs provide a novel parameterization of all internally stabilizing controllers and the system responses that they achieve. These can be combined with SLCs to provide parameterizations of constrained stabilizing controllers. We provide a catalog of useful SLCs, and show that by using SLPs with SLCs, we can parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization. Finally, we formulate the SLS problem, and show that it defines the broadest known class of constrained optimal control problems that can be solved using convex programming. We end by using the system level approach to computationally explore tradeoffs in controller performance, architecture cost, robustness and synthesis/implementation complexity
Robust Performance Guarantees for System Level Synthesis
We generalize the system level synthesis framework to systems defined by bounded causal linear operators, and use this parameterization to make connections between robust system level synthesis and the robust control literature. In particular, by leveraging results from ℒ₁ robust control, we show that necessary and sufficient conditions for robust performance with respect to causal bounded linear uncertainty in the system dynamics can be translated into convex constraints on the system responses. We exploit this connection to show that these conditions naturally allow for the incorporation of delay, sparsity, and locality constraints on the system responses and resulting controller implementation, allowing these methods to be applied to large-scale distributed control problems - to the best of our knowledge, these are the first such robust performance guarantees for distributed control systems
Robust Performance Guarantees for System Level Synthesis
We generalize the system level synthesis framework to systems defined by
bounded causal linear operators, and use this parameterization to make
connections between robust system level synthesis and classical results from
the robust control literature. In particular, by leveraging results from L1
robust control, we show that necessary and sufficient conditions for robust
performance with respect to causal bounded linear uncertainty in the system
dynamics can be translated into convex constraints on the system responses. We
exploit this connection to show that these conditions naturally allow for the
incorporation of delay, sparsity, and locality constraints on the system
responses and resulting controller implementation, allowing these methods to be
applied to large-scale distributed control problems -- to the best of our
knowledge, these are the first such robust performance guarantees for
distributed control systems.Comment: To appear at IEEE ACC 2020; added numerical exampl