In cities experiencing rapid economic growth, historic districts with rich cultural heritage are often demolished and replaced by modern high-rise buildings. This article shows the success of Singapore's urban conservation policy in preserving its historic districts in the face of a fast expanding economy and rapid urban development. A survey in the conservation areas shows that the policy has succeeded in preserving the historic old shophouses Blazer Nike Femme Bleu to a large extent. An analysis of the Basket Nike Blazer Mid use of shophouses shows that the policy has also succeeded in retaining the activities which reflect the community life in the core areas of Chinatown, Kampong Glam and Little India. This is because the policy allows for the operation of market forces which makes preservation and restoration of the old shophouses viable.
An open problem concerning the convergence of the optimal cost for the cheap-control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal-control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap-control problem without stability. Moreover, for left-invertible systems, the optimal control, state, and output for the perturbed problem tend to the optimal control, state, and output for the new problem. Also, a characterization of the Blazer Nike Homme Solde optimal cost for the latter problem is given in terms of the dissipation inequality.
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