57 research outputs found
A System Level Approach to Controller Synthesis
Biological and advanced cyber-physical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new “system level” (SL) approach involving three complementary SL elements. SL parameterizations (SLPs) provide an alternative to the Youla parameterization of all stabilizing controllers and the responses they achieve, and combine with SL constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance. SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. Finally, we formulate SL synthesis problems, which define the broadest known class of constrained optimal control problems that can be solved using convex programming
Realizability and Internal Model Control on Networks
It is proved that network realizability of controllers can be enforced
without conservatism using convex constraints on the closed loop transfer
function. Once a network realizable closed loop transfer matrix has been found,
a corresponding controller can be implemented using a network structured
version of Internal Model Control.Comment: 3 page
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
On the Equivalence of Youla, System-level and Input-output Parameterizations
A convex parameterization of internally stabilizing controllers is
fundamental for many controller synthesis procedures. The celebrated Youla
parameterization relies on a doubly-coprime factorization of the system, while
the recent system-level and input-output characterizations require no
doubly-coprime factorization but a set of equality constraints for achievable
closed-loop responses. In this paper, we present explicit affine mappings among
Youla, system-level and input-output parameterizations. Two direct implications
of the affine mappings are 1) any convex problem in Youla, system level, or
input-output parameters can be equivalently and convexly formulated in any
other one of these frameworks, including the convex system-level synthesis
(SLS); 2) the condition of quadratic invariance (QI) is sufficient and
necessary for the classical distributed control problem to admit an equivalent
convex reformulation in terms of Youla, system-level, or input-output
parameters.Comment: 8 pages, 3 figure
Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures
We consider the problem of computing optimal linear control policies for
linear systems in finite-horizon. The states and the inputs are required to
remain inside pre-specified safety sets at all times despite unknown
disturbances. In this technical note, we focus on the requirement that the
control policy is distributed, in the sense that it can only be based on
partial information about the history of the outputs. It is well-known that
when a condition denoted as Quadratic Invariance (QI) holds, the optimal
distributed control policy can be computed in a tractable way. Our goal is to
unify and generalize the class of information structures over which quadratic
invariance is equivalent to a test over finitely many binary matrices. The test
we propose certifies convexity of the output-feedback distributed control
problem in finite-horizon given any arbitrarily defined information structure,
including the case of time varying communication networks and forgetting
mechanisms. Furthermore, the framework we consider allows for including
polytopic constraints on the states and the inputs in a natural way, without
affecting convexity
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
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