Minimum entropy control for non-Newtonian mechanical systems based on pattern moving probability density evolution

Non-Newtonian mechanical systems, as a specific type of system governed by statistical laws, are commonly found in industrial production processes involving solid–liquid transitions. The challenge of describing the statistical characteristics of such systems using deterministic variables (such as state or output variables) often leads existing control methods to either ignore these systems or treat them as systems with disturbances. This approach, however, frequently results in high energy consumption within the control system. To address the system’s inherent statistical characteristics, this paper introduced a statistical variable called the pattern category variable, which replaces traditional deterministic variables in describing system motion. Additionally, a dynamic description and control framework based on probability density evolution was proposed. The conditional probability density was used as a measure for the pattern category variables, and its evolution law was derived using the principles of probability conservation and non-parametric dynamic linearization theory. Building on this, the probability density evolution of the tracking error was further determined, leading to the formulation of a minimum entropy control law based on pattern movement, accompanied by a parameter estimation algorithm. This approach transformed the control problem of non-Newtonian mechanical systems into reducing the randomness of the system’s tracking errors. Finally, the convergence and stability of both the parameter estimation algorithm and the control algorithm were validated through theoretical analysis. The effectiveness of the proposed method was demonstrated through numerical simulations.