System Level Synthesis with State and Input Constraints

Chen, Yuxiao; Anderson, James

doi:10.1109/cdc40024.2019.9029745

Cited by 17 publications

(26 citation statements)

References 14 publications

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“…Now, let y be the corresponding response of the dynamic system (17). Furthermore, define the scalar sequence s τ := P τ (y) p , i.e.…”

Section: B a Local Small Gain Theoremmentioning

confidence: 99%

“…Then, substituting the dynamics (17) into the definition (21) and using strict causality of ∆ gives us s τ +1 = P τ +1 (y) p = P τ +1 (∆(y) + w) p = P τ +1 (∆(P τ y)…”

Section: B a Local Small Gain Theoremmentioning

confidence: 99%

“…Theorem II.3. Consider system (17) and assume that ∆ satisfies ∆(x) p ≤ γ x p + β for all x ∈ n p . Then, correspondingly for all w ∈ n p , the system response y satisfies the bound…”

Section: B a Local Small Gain Theoremmentioning

confidence: 99%

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A System Level Approach to Discrete-Time Nonlinear Systems

2020

2020 American Control Conference (ACC)

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We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in discrete-time. We will show that, given a causal nonlinear discrete-time system and controller, the resulting closed-loop is a solution to a nonlinear operator equation. Conversely, any causal solution to the nonlinear operator equation is a closedloop that can be achieved by some causal controller. Moreover, solutions can be substituted into a simple dynamic controller structure, which we will refer to as a system level controller, to obtain an implementation of the unique corresponding feedback controller. System level controllers could be an attractive approach for robust nonlinear control, as we will show that even when they are parametrized with approximate solutions to the operator equation, they can still produce robustly stable closed loops. We will provide theoretical results that state how grade of approximation and robust stability of the closed loop are related. Additionally, we will explore some first applications of our results. Using the cart-pole system as an illustrative example, we will derive how to design robust discrete-time trajectory tracking controllers for continuous-time nonlinear systems. Secondly, we will introduce a particular class of system level controller that shows to be particularly useful for linear systems with actuator saturation and state constraints; The special structure of the controller allows for simple stability and performance analysis of the closed-loop in presence of disturbances. The structure also offers simple ways to do antiwindup compensation, and provides a new nonlinear approach to the constrained LQG problem. A particular application to large-scale systems with actuator saturation and safety constraints is presented in our companion paper [1].

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“…Now, let y be the corresponding response of the dynamic system (17). Furthermore, define the scalar sequence s τ := P τ (y) p , i.e.…”

Section: B a Local Small Gain Theoremmentioning

confidence: 99%

“…Then, substituting the dynamics (17) into the definition (21) and using strict causality of ∆ gives us s τ +1 = P τ +1 (y) p = P τ +1 (∆(y) + w) p = P τ +1 (∆(P τ y)…”

Section: B a Local Small Gain Theoremmentioning

confidence: 99%

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A System Level Approach to Discrete-Time Nonlinear Systems

2020

2020 American Control Conference (ACC)

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“…. A simpler control block diagram corresponding to (5). Note the single convolution zΦu according to which, after rearranging, gives…”

Section: B a Simpler Sls Controller Realizationmentioning

confidence: 99%

“…Recently, a framework named system level synthesis (SLS) was proposed to facilitate distributed controller synthesis for large-scale (networked) systems [1]- [3]. Instead of designing the controller itself, SLS directly synthesizes desired closed-loop system responses subject to system level constraints, such as localization constraints [4] and state and input constraints [5]. Using the closed-loop system response, SLS derives the optimal linear controller model, which admits multiple (mathematically equivalent) control block diagrams/state space realizations (or simply realizations) [2], [6].…”

Section: Introductionmentioning

confidence: 99%

Deployment Architectures for Cyber-Physical Control Systems

Tseng

Anderson

2020

2020 American Control Conference (ACC)

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We consider the problem of how to deploy a controller to a (networked) cyber-physical system (CPS). Controlling a CPS is an involved task, and synthesizing a controller to respect sensing, actuation, and communication constraints is only part of the challenge. In addition to controller synthesis, one should also consider how the controller will work in the CPS. Put another way, the cyber layer and its interaction with the physical layer need to be taken into account. In this work, we aim to bridge the gap between theoretical controller synthesis and practical CPS deployment. We adopt the system level synthesis (SLS) framework to synthesize a state-feedback controller and provide a deployment architecture for the standard SLS controller. Furthermore, we derive a new controller realization for open-loop stable systems and introduce four different architectures for deployment, ranging from fully centralized to fully distributed. Finally, we compare the trade-offs among them in terms of robustness, memory, computation, and communication overhead. Notation and Terminology: Let RH ∞ denote the set of stable rational proper transfer matrices, and z −1 RH ∞ ⊂ RH ∞ be the subset of strictly proper stable transfer matrices. Lower-and upper-case letters (such as x and A) denote vectors and matrices respectively, while bold lower-and upper-case characters and symbols (such as u and Φ u) are reserved for signals and transfer matrices. Let A ij be the entry of A at the i th row and j th column. We define A i as the i th row and A j the j th column of A. We use Φ u [τ ] to denote the τ th spectral element of a transfer function Φ u , i.e., Φ u = ∞ τ =0 z −τ Φ u [τ ]. We briefly summarize below the major terminology: • Controller model: a (linear) map from the state vector to the control action. • Realization: a control block diagram/state space dynamics based on some controller model. • Architecture: a cyber-physical system structure built from basic components. • Synthesize: derive a controller model (and some realization). • Deploy/Implement: map a controller model (through a realization) to an architecture.

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