In this chapter, we define a metric distance between probability distributions of unequal dimensions. Using this metric, we then address the problem of optimally approximating a high-order distribution by another one of a lower, prespecified order. It is shown that both the problem of computing the distance and of finding the optimal reduced-order approximation can be formulated as extensible bin- packing problems, and are thus NP-hard. Polynomial-time suboptimal algorithms are provided for both problems.

Inspec keywords: stochastic processes; suboptimal control; statistical distributions; computational complexity; optimisation; reduced order systems; bin packing

Other keywords: NP-hard problem; optimal reduced-order approximation; probability distribution; high-order distribution; stochastic process; metric distance; mutual information maximization; unequal dimension; random variable; polynomial-time suboptimal algorithm; order reduction; bin packing problem

Subjects: Control system analysis and synthesis methods