Abstract

This talk marks the inception of the Imperial-Cambridge-Oxford Seminar Series on Control for Energy and Sustainability. The role of Optimal Control in the overall research programme of the participating universities will be described. A review will also be provided of recent theoretical developments in state constrained optimal control – currently one of the most active research areas in the field. Key analytic tools (regarding deviation of necessary conditions of optimality, characterizing the cost-to-go as a solution to the Bellman equation, problem reformation to ensure optimality conditions are non-degenerate and to ensure improved condition for numerical computation, etc.) are estimates on the ‘distance’ of an arbitrary trajectory to the set of trajectories that satisfy the state constraint. We review the history of such estimates and explain their significance. The situation in which the state constraint set has a smooth boundary is well understood. But that in which the state constraint set has corners is much more problematic. Here, claimed estimates, of longstanding, have recently been revealed as false, and must be replaced by estimates of a quite unexpected nature. We discuss some implications for the field.