Nonlinear Circle-Criterion Observer Design for an Electrochemical Battery Model

Constrained State Estimation for Nonlinear Systems: A Redesign Approach Based on Convexity

“…In order to use ψ k+1 defined in (38), we need to be able to make (at most) θ + 1 recursive computations at each discrete step k. Note, however, that in this case, the Lyapunov function decreases even if we perform less than θ + 1 steps. Therefore, in case of limited computational power, it is still interesting…”

“…4) Design the function M k+1 as in (31), and select γ d > 0 small enough. 5) Design the function ψ k+1 as in (30) with ψ k+1,i defined in (35); alternatively, if outer semi-continuity is sought, select ψ k+1 as in (38), with ψ k+1 defined in (37) and ψ k+1,i in (36). 6) Select θ large enough and run the new observer (25) with Gm defined as in ( 27) and ψ k+1 as in the previous step, and with an initial condition x(0) ∈ X .…”

“…To give an example, when the concentrations of Lithium-ion in the electrodes of an electrochemical battery are estimated, e.g. [38], it may occur that the estimated concentrations generated by the observer are negative for some time, which is physically impossible. This is the case in general for positive systems (see, e.g., [39]).…”

A novel charged state prediction method of the lithium ion battery packs based on the composite equivalent modeling and improved splice Kalman filtering algorithm

“…L represents the dimension of the state variable and its value is 3. Its relationship satisfies λ+L=3, the calculation process of which is shown in Equation (14).…”

“…Since the battery charged state is a physical quantity that cannot be measured directly [10,11], it should be estimated by the information such as voltage, current, internal resistance and temperature that are related to the operating state of the lithium ion battery packs, so its prediction purpose can be turned into a model parameter reorganization problem according to its special impact on the charged state estimation accuracy [12]. Some adaptive estimation methods have been proposed to be suitable for different application backgrounds of the lithium ion batteries [13][14][15][16], including electric vehicles, substations, smart grids and financial uninterruptible power systems. These approaches can be divided into three categories: simple calculation, data-driven and battery-based modeling methods [17][18][19][20].…”