Interval Observers for Uncertain Nonlinear Systems. Application to Bioreactors

This paper is about state estimation for nonlinear uncertain continuous-time systems in a bounded-error context. We introduce a method for designing a guaranteed interval observer which is based on (i) the application of Müller’s theorem for bracketing the solution of ordinary differential equations in a way which ensures the positivity of the observation error, (ii) the analysis of the monotonicity of each component of system field vectors with respect to both the uncertain parameters and state variables and (iii) the choice of a tailor-made observation gain matrix in order to ensure that the observation error converges to the interior of a bounded box. The set of state estimation obtained in this context is a guaranteed approximation of the real solution set in the sense that no solution can be lost.