Identification of switched ARX models via convex optimization and expectation maximization

• SON-EM, a novel methodology to parameter identification of SARX models is presented.
• The proposed method combines convex optimization and expectation maximization (EM).
• Another algorithm is introduced to estimate the cardinality of the submodel set.
• SON-EM outperforms recently developed identification methods on a simulated system.
• The method is illustrated on experimental dataset of diauxic bacterial growth.

This article addresses the problem of parameter identification for Switched affine AutoRegressive models with eXogenous inputs (SARX). The system includes continuous domain states that depend on discrete time-varying parameters. The identification of such systems typically results in non-convex problems that could be tackled as a mixed integer program. However, in this case, the computational complexity would be intractable in many practical applications. Another approach involves heuristics in order to deliver approximate solutions. This article proposes a three-step method based on solving a regularized convex optimization problem, followed by a clustering step, yielding a partial solution to the problem. When substituted back into the original problem, the partial solution renders it convex. Finally, this convex problem is solved in the third step, yielding an approximate solution. It is found that each step significantly improves the parameter estimation results on the systems considered. A beneficial property of the method is that it relies upon only one scalar tuning parameter, to which the final results are not highly sensitive. The performance of the algorithm is compared with other methods on a simulated system, and illustrated in an experimental biological dataset of diauxic bacterial growth.