The effects of synthesis parameters on the shape of gold nanoparticles (Au NPs) and their growth are investigated. A ternary space to study their shape transitions is reported for the first time. A growth mechanism based on supersaturation is proposed.
Explicit constrained control is relatively simple when a controlled contractive set is available. However, the complexity of the explicit controller will depend on the complexity of the controlled contractive set. The ability to design a low complexity controlled contractive set is therefore desirable. Most methods for finding controlled contractive sets either assume the use of a constant linear state feedback, or is based on reachable set computations. In the first case, the assumption of a constant linear state feedback is restrictive (as MPC controllers for linear systems are typically piecewise affine), and in the second case the complexity of the controlled contractive set may be very high. Initial results on the construction of low complexity controlled contractive sets without assuming linear state feedback were reported at the IFAC World Congress in 2014. The present paper addresses shortcomings in the previous results, including the ability to handle identical modes in series (corresponding to a non-diagonalizable A matrix) and oscillatory modes. The paper suggests a method to find a flexible complexity controlled contractive set.
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