Solar activity shows an 11-year (quasi)periodicity with a pronounced, but limited variability of the cycle amplitudes. The properties of active region (AR) emergence play an important role in the modulation of solar cycles and are our central concern in building a model for predicting future cycle(s) in the framework of the Babcock–Leighton (BL)-type dynamo. The emergence of ARs has the property that strong cycles tend to have higher mean latitudes and lower tilt angle coefficients. Their non-linear feedbacks on the solar cycle are referred to as latitudinal quenching and tilt quenching, respectively. Meanwhile, the stochastic properties of AR emergence, e.g., rogue ARs, limit the scope of the solar cycle prediction. For physics-based prediction models of the solar cycle, we suggest that uncertainties in both the observed magnetograms assimilated as the initial field and the properties of the AR emergence should be taken into account.

This paper is concerned with the sampled-data based adaptivelinear quadratic (LQ) control of hybrid systems with bothunmeasurable Markov jump processes and stochastic noises.By the least matching error estimation algorithm, parameter estimatesare presented. By a double-step (DS) sampling approach and the certaintyequivalence principle, a sampled-data based adaptive LQ control isdesigned. The DS-approach is characterized by a comparatively largeestimation step for parameter estimation and a sufficient small controlstep for control updating. Under mild conditions, the closed-loop systemis shown to be stable. It is found that the key factor determining theperformance index is the estimation step rather than the control step.When the estimation step becomes too small, the system performance willbecome worse. When the estimation step is fixed, the system performancecan indeed be improved by reducing the control step, but cannot reachthe optimal value. The index difference between the sampled-data basedadaptive LQ control and the conventional LQ optimal control is asymptoticallybounded by a constant depending on the estimation step and the prioriinformation of the parameter set.