# Scalable computation for optimal control of cascade systems with constraints

## TL;DR

This paper introduces a scalable, distributed method for solving large-scale finite-horizon optimal control problems in cascade systems, with computation cost scaling linearly with the number of sub-systems.

## Contribution

It develops a novel interior-point approach exploiting problem structure for efficient, distributed computation in cascade control systems.

## Key findings

- Computation cost scales linearly with the number of sub-systems.
- Method is suitable for distributed implementation with low communication overhead.
- Example demonstrates application to automated irrigation channel dynamics.

## Abstract

A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.