# Design of Affine Controllers via Convex Optimization

@article{Skaf2010DesignOA, title={Design of Affine Controllers via Convex Optimization}, author={Jo{\"e}lle Skaf and Stephen P. Boyd}, journal={IEEE Transactions on Automatic Control}, year={2010}, volume={55}, pages={2476-2487} }

We consider a discrete-time time-varying linear dynamical system, perturbed by process noise, with linear noise corrupted measurements, over a finite horizon. We address the problem of designing a general affine causal controller, in which the control input is an affine function of all previous measurements, in order to minimize a convex objective, in either a stochastic or worst-case setting. This controller design problem is not convex in its natural form, but can be transformed to an…

## 127 Citations

Nonlinear Q-Design for Convex Stochastic Control

- MathematicsIEEE Transactions on Automatic Control
- 2009

A version of the Q-design method that can be used to design nonlinear dynamic controllers for a discrete-time linear time-varying plant, with convex cost and constraint functions and arbitrary disturbance distribution is described.

An Efficient Method to Estimate the Suboptimality of Affine Controllers

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2011

Using duality arguments and by imposing an affine structure on the dual variables, this work provides an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data.

Robust affine control of linear stochastic systems

- Mathematics
- 2017

This work expands on the previous investigations on finite horizon covariance control by addressing the robustness issue and the possibility that the full state may not be available, therefore enabling the steering of the state-control trajectory density in the presence of disturbances under partial observation.

Constrained minimum variance control for discrete-time stochastic linear systems

- Mathematics, Computer ScienceSyst. Control. Lett.
- 2018

Convex Optimization for Finite-Horizon Robust Covariance Control of Linear Stochastic Systems

- MathematicsSIAM J. Control. Optim.
- 2021

This work develops a computationally tractable procedure for designing affine control policies, in the sense that the parameters of the policy that guarantees the aforementioned performance specifications are obtained as solutions to an explicit convex program.

Covariance control for discrete-time stochastic linear systems with incomplete state information

- Mathematics2017 American Control Conference (ACC)
- 2017

Under the assumption that the class of admissible control policies for this stochastic optimal control problem is comprised of sequences of non-anticipative (causal) control laws that can be expressed as linear combinations of the past and present output measurements of the system, the covariance control problem can be reduced to a finite-dimensional, deterministic nonlinear program with a convex performance index.

Dynamic Output Feedback Control of the Liouville Equation for Discrete-Time SISO Linear Systems

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2019

A systematic procedure is proposed for the characterization of a dynamic output feedback policy that will transfer the output of the system, which is a known Gaussian random variable, to a goal Gaussian distribution after a finite number of stages.

Stochastic linear systems subject to constraints

- Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

It is shown that the stochastic optimal control problem is equivalent to a deterministic nonlinear program, which, under a judicious choice of the decision variable, can be brought to a form in which its performance index is a convex, quadratic function subject to both equality and inequalityquadratic constraints.

2 5 N ov 2 01 8 Robust affine control of linear stochastic systems

- Mathematics
- 2018

In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded…

Finite-horizon covariance control for discrete-time stochastic linear systems subject to input constraints

- Mathematics, Computer ScienceAutom.
- 2018

## References

SHOWING 1-10 OF 98 REFERENCES

Control of Uncertainty-Affected Discrete Time Linear Systems via Convex Programming

- Mathematics
- 2006

In [1], we have demonstrated that robust optimization of linear finite-horizon control in a discrete time linear dynamical system affected by uncertain disturbances becomes computationally tractable…

Output feedback receding horizon control of constrained systems

- MathematicsInt. J. Control
- 2007

A time-invariant control law is developed that can be computed by solving a finite-dimensional tractable optimization problem at each time step that guarantees that the closed-loop system satisfies the constraints for all time.

Optimization over state feedback policies for robust control with constraints

- MathematicsAutom.
- 2006

Input-to-state stability of robust receding horizon control with an expected value cost

- MathematicsAutom.
- 2008

Convex analysis of output feedback control problems: robust stability and performance

- MathematicsIEEE Trans. Autom. Control.
- 1996

This paper addresses the problem of optimal H/sub 2/ control by output feedback. Necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in…

Closed-loop stochastic dynamic process optimization under input and state constraints

- Computer ScienceProceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
- 2002

This approach to constrained dynamic optimization and control distinguishes itself from any existing open-loop strategy by explicitly predicting the closed-loop behavior of the plant under the influence of stochastic disturbances.

Optimality of affine policies in multi-stage robust optimization

- Computer ScienceProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
- 2009

This paper proves the optimality of disturbance-affine control policies in the context of onedimensional, box-constrained, multi-stage robust optimization, and entails efficient algorithms for the case of piecewise affine state costs.

Linear controller design: limits of performance via convex optimization

- Computer Science
- 1990

An approach to the analysis and design of linear control systems based on numerical convex optimization over closed-loop maps is presented, and it is shown that many performance specifications have natural and useful geometric interpretations, and the notion of a closed- loop convex design specification is defined.

Optimal control: linear quadratic methods

- Mathematics
- 1990

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory…

Minimax approaches to robust model predictive control

- Mathematics, Computer Science
- 2003

It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.